Dietmar Salamon's Books

J-holomorphic Curves and Symplectic Topology

By: Dusa McDuff,Dietmar Salamon

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J-holomorphic Curves and Symplectic Topology

By: Dusa McDuff,Dietmar Salamon

The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology.

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Page Count

744

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821887467

ISBN 13

9780821887462

Introduction to Symplectic Topology

By: Dusa McDuff,Dietmar Salamon

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Introduction to Symplectic Topology

By: Dusa McDuff,Dietmar Salamon

Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. A significantly revised second edition was published in 1998 introducing new sections and updates on the fast-developing area. This new third edition includes updates and new material to bring the book right up-to-date.

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Page Count

632

Publisher

Oxford University Press

Published Date

ISBN 10

0192514016

ISBN 13

9780192514011

Functional Analysis

By: Theo Bühler,Dietmar A. Salamon

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Functional Analysis

By: Theo Bühler,Dietmar A. Salamon

It begins in Chapter 1 with an introduction to the necessary foundations, including the Arzelà–Ascoli theorem, elementary Hilbert space theory, and the Baire Category Theorem. Chapter 2 develops the three fundamental principles of functional analysis (uniform boundedness, open mapping theorem, Hahn–Banach theorem) and discusses reflexive spaces and the James space. Chapter 3 introduces the weak and weak topologies and includes the theorems of Banach–Alaoglu, Banach–Dieudonné, Eberlein–Šmulyan, Kre&ibreve;n–Milman, as well as an introduction to topological vector spaces and applications to ergodic theory. Chapter 4 is devoted to Fredholm theory. It includes an introduction to the dual operator and to compact operators, and it establishes the closed image theorem. Chapter 5 deals with the spectral theory of bounded linear operators. It introduces complex Banach and Hilbert spaces, the continuous functional calculus for self-adjoint and normal operators, the Gelfand spectrum, spectral measures, cyclic vectors, and the spectral theorem. Chapter 6 introduces unbounded operators and their duals. It establishes the closed image theorem in this setting and extends the functional calculus and spectral measure to unbounded self-adjoint operators on Hilbert spaces. Chapter 7 gives an introduction to strongly continuous semigroups and their infinitesimal generators. It includes foundational results about the dual semigroup and analytic semigroups, an exposition of measurable functions with values in a Banach space, and a discussion of solutions to the inhomogeneous equation and their regularity properties. The appendix establishes the equivalence of the Lemma of Zorn and the Axiom of Choice, and it contains a proof of Tychonoff's theorem. With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a one-or-two-semester course on functional analysis for beginning graduate students. Prerequisites are first-year analysis and linear algebra, as well as some foundational material from the second-year courses on point set topology, complex analysis in one variable, and measure and integration.

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482

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147044190X

ISBN 13

9781470441906

Combinatorial Floer Homology

By: Vin de Silva,Joel W. Robbin,Dietmar A. Salamon

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Combinatorial Floer Homology

By: Vin de Silva,Joel W. Robbin,Dietmar A. Salamon

The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented -manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology. Their proof uses a formula for the Viterbo-Maslov index for a smooth lune in a -manifold.

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Page Count

126

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821898868

ISBN 13

9780821898864

The Moment-Weight Inequality and the Hilbert–Mumford Criterion

GIT from the Differential Geometric Viewpoint

By: Valentina Georgoulas,Joel W. Robbin,Dietmar Arno Salamon

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The Moment-Weight Inequality and the Hilbert–Mumford Criterion

GIT from the Differential Geometric Viewpoint

By: Valentina Georgoulas,Joel W. Robbin,Dietmar Arno Salamon

This book provides an introduction to geometric invariant theory from a differential geometric viewpoint. It is inspired by certain infinite-dimensional analogues of geometric invariant theory that arise naturally in several different areas of geometry. The central ingredients are the moment-weight inequality relating the Mumford numerical invariants to the norm of the moment map, the negative gradient flow of the moment map squared, and the Kempf--Ness function. The exposition is essentially self-contained, except for an appeal to the Lojasiewicz gradient inequality. A broad variety of examples illustrate the theory, and five appendices cover essential topics that go beyond the basic concepts of differential geometry. The comprehensive bibliography will be a valuable resource for researchers. The book is addressed to graduate students and researchers interested in geometric invariant theory and related subjects. It will be easily accessible to readers with a basic understanding of differential geometry and does not require any knowledge of algebraic geometry.

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Page Count

193

Publisher

Springer Nature

Published Date

ISBN 10

3030893006

ISBN 13

9783030893002

Introduction to Symplectic Topology

By: Dusa McDuff,Dietmar Salamon

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Introduction to Symplectic Topology

By: Dusa McDuff,Dietmar Salamon

This first edition of this book quickly became an established text in this fast-developing branch of mathematics. This second edition has been significantly revised and expanded. It includes a section on new developments and an expanded discussion of Taubes' and Donaldson's recent results.

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Page Count

500

Publisher

Oxford University Press

Published Date

ISBN 10

0198504519

ISBN 13

9780198504511

Combinatorial Floer Homology

By: Vin de Silva,Joel W. Robbin,Dietmar A. Salamon

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Combinatorial Floer Homology

By: Vin de Silva,Joel W. Robbin,Dietmar A. Salamon

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Page Count

126

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821898868

ISBN 13

9780821898864

$J$-Holomorphic Curves and Quantum Cohomology

By: Dusa McDuff,Dietmar Salamon

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$J$-Holomorphic Curves and Quantum Cohomology

By: Dusa McDuff,Dietmar Salamon

J -holomorphic curves revolutionized the study of symplectic geometry when Gromov first introduced them in 1985. Through quantum cohomology, these curves are now linked to many of the most exciting new ideas in mathematical physics. This book presents the first coherent and full account of the theory of J -holomorphic curves, the details of which are presently scattered in various research papers. The first half of the book is an expository account of the field, explaining the main technical aspects. McDuff and Salamon give complete proofs of Gromov's compactness theorem for spheres and of the existence of the Gromov-Witten invariants. The second half of the book focuses on the definition of quantum cohomology. The authors establish that the quantum multiplication exists and is associative on appropriate manifolds. They then describe the Givental-Kim calculation of the quantum cohomology of flag manifolds, leading to quantum Chern classes and Witten's calculation for Grassmanians, which relates to the Verlinde algebra. The Dubrovin connection, Gromov-Witten potential on quantum cohomology, and curve counting formulas are also discussed.

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Page Count

220

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821803328

ISBN 13

9780821803325

Functional Analysis

By: Theo Bühler,Dietmar A. Salamon

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Functional Analysis

By: Theo Bühler,Dietmar A. Salamon

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Solve jigsaw puzzle

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Page Count

482

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147044190X

ISBN 13

9781470441906

Book's by Dietmar Salamon

J-holomorphic Curves and Symplectic Topology

J-holomorphic Curves and Symplectic Topology

Introduction to Symplectic Topology

Introduction to Symplectic Topology

Functional Analysis

Functional Analysis

Combinatorial Floer Homology

Combinatorial Floer Homology

The Moment-Weight Inequality and the Hilbert–Mumford Criterion

The Moment-Weight Inequality and the Hilbert–Mumford Criterion

Introduction to Symplectic Topology

Introduction to Symplectic Topology

Combinatorial Floer Homology

Combinatorial Floer Homology

$J$-Holomorphic Curves and Quantum Cohomology

$J$-Holomorphic Curves and Quantum Cohomology

Functional Analysis

Functional Analysis

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