Peter Kronheimer's Books

Monopoles and Three-Manifolds

By: Peter Kronheimer,Tomasz Mrowka

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This 2007 book provides a comprehensive treatment of Floer homology, based on the Seiberg-Witten equations. Suitable for beginning graduate students and researchers in the field, this book provides a full discussion of a central part of the study of the topology of manifolds.

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796

Published Date

ISBN 10

052188022X

ISBN 13

9780521880220

Grid Homology for Knots and Links

By: Peter S. Ozsvath,András I. Stipsicz,Zoltan Szabo

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Grid Homology for Knots and Links

By: Peter S. Ozsvath,András I. Stipsicz,Zoltan Szabo

Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.

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Page Count

410

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470434423

ISBN 13

9781470434427

The Ergodic Theory of Discrete Groups

By: Peter J. Nicholls

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The Ergodic Theory of Discrete Groups

By: Peter J. Nicholls

The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. There has been a great resurgence of interest in the field, due in large measure to the pioneering work of Dennis Sullivan. Tools have been developed and applied with outstanding success to many deep problems. The ergodic theory of discrete groups has become a substantial field of mathematical research in its own right, and it is the aim of this book to provide a rigorous introduction from first principles to some of the major aspects of the theory. The particular focus of the book is on the remarkable measure supported on the limit set of a discrete group that was first developed by S. J. Patterson for Fuchsian groups, and later extended and refined by Sullivan.

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Page Count

237

Publisher

Cambridge University Press

Published Date

ISBN 10

0521376742

ISBN 13

9780521376747

The Subgroup Structure of the Finite Classical Groups

By: Peter B. Kleidman,Martin W. Liebeck

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The Subgroup Structure of the Finite Classical Groups

By: Peter B. Kleidman,Martin W. Liebeck

With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.

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Page Count

317

Publisher

Cambridge University Press

Published Date

ISBN 10

052135949X

ISBN 13

9780521359498

Knots and Links

By: Peter R. Cromwell

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Knots and Links

By: Peter R. Cromwell

A richly illustrated 2004 textbook on knot theory; minimal prerequisites but modern in style and content.

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Page Count

356

Publisher

Cambridge University Press

Published Date

ISBN 10

0521548314

ISBN 13

9780521548311

Invariance Theory

The Heat Equation and the Atiyah-Singer Index Theorem

By: Peter B. Gilkey

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Invariance Theory

The Heat Equation and the Atiyah-Singer Index Theorem

By: Peter B. Gilkey

This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.

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Page Count

534

Publisher

CRC Press

Published Date

ISBN 10

0849378745

ISBN 13

9780849378744

The Aesthetics of Resistance, Volume II

A Novel, Volume 2

By: Peter Weiss

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The Aesthetics of Resistance, Volume II

A Novel, Volume 2

By: Peter Weiss

A major literary event, the publication of the second volume of Peter Weiss's three-volume novel The Aesthetics of Resistance makes one of the towering works of twentieth-century German literature available to English-speaking readers for the first time. The crowning achievement of Peter Weiss, the internationally renowned writer best known for his play Marat/Sade, The Aesthetics of Resistance spans the period from the late 1930s to World War II, dramatizing antifascist resistance and the rise and fall of proletarian political parties in Europe. Volume II, initially published in 1978, opens with the unnamed narrator in Paris after having retreated from the front lines of the Spanish Civil War. From there, he moves on to Stockholm, where he works in a factory, becomes involved with the Communist Party, and meets Bertolt Brecht. Featuring the narrator's extended meditations on paintings, sculpture, and literature, the novel teems with characters, almost all of whom are based on historical figures. Throughout, the narrator explores the affinity between political resistance and art—the connection at the heart of Weiss's novel. Weiss suggests that meaning lies in embracing resistance, no matter how intense the oppression, and that we must look to art for new models of political action and social understanding. The Aesthetics of Resistance is one of the truly great works of postwar German literature and an essential resource for understanding twentieth-century German history.

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Page Count

252

Publisher

Duke University Press

Published Date

ISBN 10

1478007567

ISBN 13

9781478007562

Bordered Heegaard Floer Homology

By: Robert Lipshitz,Peter Ozsváth,Dylan P. Thurston

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Bordered Heegaard Floer Homology

By: Robert Lipshitz,Peter Ozsváth,Dylan P. Thurston

The authors construct Heegaard Floer theory for 3-manifolds with connected boundary. The theory associates to an oriented, parametrized two-manifold a differential graded algebra. For a three-manifold with parametrized boundary, the invariant comes in two different versions, one of which (type D) is a module over the algebra and the other of which (type A) is an A∞ module. Both are well-defined up to chain homotopy equivalence. For a decomposition of a 3-manifold into two pieces, the A∞ tensor product of the type D module of one piece and the type A module from the other piece is ^HF of the glued manifold. As a special case of the construction, the authors specialize to the case of three-manifolds with torus boundary. This case can be used to give another proof of the surgery exact triangle for ^HF. The authors relate the bordered Floer homology of a three-manifold with torus boundary with the knot Floer homology of a filling.

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Page Count

294

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470428881

ISBN 13

9781470428884

Projective Representations of the Symmetric Groups

Q-functions and Shifted Tableaux

By: Peter Norman Hoffman,J. F. Humphreys

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Projective Representations of the Symmetric Groups

Q-functions and Shifted Tableaux

By: Peter Norman Hoffman,J. F. Humphreys

The study of the symmetric groups forms one of the basic building blocks of modern group theory. This book presents information currently known on the projective representations of the symmetric and alternating groups. Special emphasis is placed on the theory of Q-functions and skew Q-functions.

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Page Count

322

Publisher

Oxford University Press

Published Date

ISBN 10

0198535562

ISBN 13

9780198535560

Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor

By: Peter B. Gilkey

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Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor

By: Peter B. Gilkey

A central problem in differential geometry is to relate algebraic properties of the Riemann curvature tensor to the underlying geometry of the manifold. The full curvature tensor is in general quite difficult to deal with. This book presents results about the geometric conse-quences that follow if various natural operators defined in terms of the Riemann curvature tensor (the Jacobi operator, the skew-symmetric curvature operator, the Szabo operator, and higher order generalizations) are assumed to have constant eigenvalues or constant Jordan normal form in the appropriate domains of definition. The book presents algebraic preliminaries and various Schur type problems; deals with the skew-symmetric curvature operator in the real and complex settings and provides the classification of algebraic curvature tensors whos skew-symmetric curvature has constant rank 2 and constant eigenvalues; discusses the Jacobi operator and a higher order generalization and gives a unified treatment of the Osserman conjecture and related questions; and establishes the results from algebraic topology that are necessary for controlling the eigenvalue structures. An extensive bibliography is provided. Results are described in the Riemannian, Lorentzian, and higher signature settings, and many families of examples are displayed.

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Page Count

316

Publisher

World Scientific

Published Date

ISBN 10

9810247524

ISBN 13

9789810247522

Oligomorphic Permutation Groups

By: Peter J. Cameron

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Oligomorphic Permutation Groups

By: Peter J. Cameron

The study of permutations groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. This book discusses such structures, their substructures and their automorphism groups using a wide range of techniques.

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Page Count

172

Publisher

Cambridge University Press

Published Date

ISBN 10

0521388368

ISBN 13

9780521388368

Controlling Administrative Power

An Historical Comparison

By: Peter Cane

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Controlling Administrative Power

An Historical Comparison

By: Peter Cane

An historical and comparative explanation of some puzzling differences between the administrative law of England, the USA and Australia.

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609

Publisher

Cambridge University Press

Published Date

ISBN 10

1107146356

ISBN 13

9781107146358

The Separation of Powers and Legislative Interference in Judicial Process

Constitutional Principles and Limitations

By: Peter Gerangelos

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The Separation of Powers and Legislative Interference in Judicial Process

Constitutional Principles and Limitations

By: Peter Gerangelos

This book examines the constitutional principles governing the relationship between legislatures and courts at that critical crossroads of their power where legislatures may seek to intervene in the judicial process, or to interfere with judicial functions, to secure outcomes consistent with their policy objectives or interests. Cases of high political moment are usually involved, where the temptation, indeed political imperative, for legislatures to intervene can be overwhelming. Although the methods of intervention are various, ranging from the direct and egregious to the subtle and imperceptible, unbridled legislative power in this regard has been a continuing concern in all common law jurisdictions. Prominent examples include direct legislative interference in pending cases, usurpation of judicial power by legislatures, limitations on the jurisdiction of courts, strategic amendments to law applicable to cases pending appeal, and attempts directly to overturn court decisions in particular cases. Because the doctrine of the separation of powers, as an entrenched constitutional rule, is a major source of principle, the book will examine in detail the jurisprudence of the United States and Australia in particular. These jurisdictions have identical constitutional provisions entrenching that doctrine as well as the most developed jurisprudence on this point. The legal position in the United Kingdom, which does not have an entrenched separation of powers doctrine, will be examined as a counterpoint. Other relevant jurisdictions (such as Canada, Ireland and India) are also examined in the context of particular principles, particularly when their respective jurisprudence is rather more developed on discrete points. The book examines how the relevant constitutional principles strive to maintain the primacy of the law-making role of the legislature in a representative democracy and yet afford the decisional independence of the judiciary that degree of protection essential to protect it from the legislature's 'impetuous vortex', to borrow the words of James Madison from The Federalist (No 48).

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Page Count

360

Publisher

Bloomsbury Publishing

Published Date

ISBN 10

1847315003

ISBN 13

9781847315007

Secret Treaties and Other International Agreements

By: Peter C. Lundy

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Secret Treaties and Other International Agreements

By: Peter C. Lundy

In Secret Treaties and Other International Agreements, Peter C. Lundy explores the relationship between formal treaties under international law and documents of lesser status, commonly known as memorandums of understanding. The book critically examines the gaps in diplomatic policy, with a particular focus on the Australian Government’s casual approach to these non-treaty documents. Featuring original copies of the historic Five Eyes Agreement between the British Government and the United States, the book offers a unique perspective on significant international relations. Lundy delves into the consequences of relying on such agreements, notably highlighting the atomic bomb tests at Maralinga in South Australia. Beyond identifying these issues, the book proposes methods to address the inconsistencies in how the Australian Government handles non-treaty documents. It also compares the approaches of other nations, including the United States, the United Kingdom, and the European Community, offering solutions to the challenges Australia has faced in the past.

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Page Count

434

Publisher

Australian Self Publishing Group

Published Date

ISBN 10

1923250280

ISBN 13

9781923250284

The Constitution of the Commonwealth of Australia

By: Nicholas Aroney,Peter Gerangelos,Sarah Murray,James Stellios

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The Constitution of the Commonwealth of Australia

By: Nicholas Aroney,Peter Gerangelos,Sarah Murray,James Stellios

This book provides an engaging and distinctive treatment for anyone seeking to understand the significance and interpretation of the Constitution.

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Page Count

697

Publisher

Cambridge University Press

Published Date

ISBN 10

0521759188

ISBN 13

9780521759182

Book's by Peter Kronheimer

Monopoles and Three-Manifolds

Monopoles and Three-Manifolds

Grid Homology for Knots and Links

Grid Homology for Knots and Links

The Ergodic Theory of Discrete Groups

The Ergodic Theory of Discrete Groups

The Subgroup Structure of the Finite Classical Groups

The Subgroup Structure of the Finite Classical Groups

Knots and Links

Knots and Links

Invariance Theory

Invariance Theory

The Aesthetics of Resistance, Volume II

The Aesthetics of Resistance, Volume II

Bordered Heegaard Floer Homology

Bordered Heegaard Floer Homology

Projective Representations of the Symmetric Groups

Projective Representations of the Symmetric Groups

Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor

Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor

Oligomorphic Permutation Groups

Oligomorphic Permutation Groups

Controlling Administrative Power

Controlling Administrative Power

The Separation of Powers and Legislative Interference in Judicial Process

The Separation of Powers and Legislative Interference in Judicial Process

Secret Treaties and Other International Agreements

Secret Treaties and Other International Agreements

The Constitution of the Commonwealth of Australia

The Constitution of the Commonwealth of Australia

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