An introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry. One of the main motivations, and a major source of examples, is string theory, where orbifolds play an important role. The subject is first developed following the classical description analogous to manifold theory, after which the book branches out to include the useful description of orbifolds provided by groupoids, as well as many examples in the context of algebraic geometry. Classical invariants such as de Rham cohomology and bundle theory are developed, a careful study of orbifold morphisms is provided, and the topic of orbifold K-theory is covered. The heart of this book, however, is a detailed description of the Chen-Ruan cohomology, which introduces a product for orbifolds and has had significant impact. The final chapter includes explicit computations for a number of interesting examples.
This book is an excellent illustration of the versatility of Algebraic Topology interacting with other areas in Mathematics and Physics. Topics discussed in this volume range from classical Differential Topology and Homotopy Theory (Kervaire invariant one problem) to more recent lines of research such as Topological Quantum Field Theory (string theory). Likewise, alternative viewpoints on classical problems in Global Analysis and Dynamical Systems are developed (a spectral sequence approach to normal form theory). This collection of papers is based on talks at the conference on the occasion of Sam Gitler's 70th birthday (December, 2003). The variety of topics covered in this book reflects the many areas where Sam Gitler's contributions have had an impact.
This book publishes papers originally presented at a conference on the Mathematical Aspects of Orbifold String Theory, hosted by the University of Wisconsin-Madison. It contains a great deal of information not fully covered in the published literature and showcases the current state of the art in orbital string theory. The subject of orbifolds has a long prehistory, going back to the work of Thurston and Haefliger, with roots in the theory of manifolds, group actions, and foliations. The recent explosion of activity on the topic has been powered by applications of orbifolds to moduli problems and quantum field theory. The present volume presents an interdisciplinary look at orbifold problems. Topics such as stacks, vertex operator algebras, branes, groupoids, K-theory and quantum cohomology are discussed. The book reflects the thinking of distinguished investigators working in the areas of mathematical physics, algebraic geometry, algebraic topology, symplectic geometry and representation theory. By presenting the work of a broad range of mathematicians and physicists who use and study orbifolds, it familiarizes readers with the various points of view and types of results the researchers bring to the subject.
This volume presents the proceedings from the conference on ``Topology, Geometry, and Algebra: Interactions and New Directions'' held in honor of R. James Milgram at Stanford University in August 1999. The meeting brought together distinguished researchers from a variety of areas related to algebraic topology and its applications. Papers in the book present a wide range of subjects, reflecting the nature of the conference. Topics include moduli spaces, configuration spaces, surgerytheory, homotopy theory, knot theory, group actions, and more. Particular emphasis was given to the breadth of interaction between the different areas.
This volume presents the proceedings from the conference on ''Topology, Geometry, and Algebra: Interactions and New Directions'' held in honor of R. James Milgram at Stanford University in August 1999. The meeting brought together distinguished researchers from a variety of areas related to algebraic topology and its applications. Papers in the book present a wide range of subjects, reflecting the nature of the conference. Topics include moduli spaces, configuration spaces, surgerytheory, homotopy theory, knot theory, group actions, and more. Particular emphasis was given to the breadth of interaction between the different areas.
This book is the result of a conference held to examine developments in homotopy theory in honor of Samuel Gitler in July 1993 (Cocoyoc, Mexico). It includes several research papers and three expository papers on various topics in homotopy theory. The research papers discuss the following: BL application of homotopy theory to group theory BL fiber bundle theory BL homotopy theory The expository papers consider the following topics: BL the Atiyah-Jones conjecture (by C. Boyer) BL classifying spaces of finite groups (by J. Martino) BL instanton moduli spaces (by J. Milgram) Homotopy Theory and Its Applications offers a distinctive account of how homotopy theoretic methods can be applied to a variety of interesting problems.
AMS-IMS-SIAM Joint Summer Research Conference on Q-Series, Combinatorics, and Computer Algebra, June 21-25, 1998, Mount Holyoke College, South Hadley, MA
AMS-IMS-SIAM Joint Summer Research Conference on Q-Series, Combinatorics, and Computer Algebra, June 21-25, 1998, Mount Holyoke College, South Hadley, MA
This volume presents the proceedings of the Summer Research Conference on q-series and related topics held at Mount Holyoke College (Hadley, Massachusetts). All of the papers were contributed by participants and offer original research. Articles in the book reflect the diversity of areas that overlap with q-series, as well as the usefulness of q-series across the mathematical sciences. The conference was held in honour of Richard Askey on the occasion of his 65th birthday.
Cohomology, Group Actions, and Topology : Summer Research Institute on Cohomology, Representations, and Actions of Finite Groups, July 7-27, 1996, University of Washington, Seattle
Cohomology, Group Actions, and Topology : Summer Research Institute on Cohomology, Representations, and Actions of Finite Groups, July 7-27, 1996, University of Washington, Seattle
This volume combines contributions in topology and representation theory that reflect the increasingly vigorous interactions between these areas. Topics such as group theory, homotopy theory, cohomology of groups, and modular representations are covered. All papers have been carefully refereed and offer lasting value.
This book is an excellent illustration of the versatility of Algebraic Topology interacting with other areas in Mathematics and Physics. Topics discussed in this volume range from classical Differential Topology and Homotopy Theory (Kervaire invariant one problem) to more recent lines of research such as Topological Quantum Field Theory (string theory). Likewise, alternative viewpoints on classical problems in Global Analysis and Dynamical Systems are developed (a spectral sequence approach to normal form theory). This collection of papers is based on talks at the conference on the occasion of Sam Gitler's 70th birthday (December, 2003). The variety of topics covered in this book reflects the many areas where Sam Gitler's contributions have had an impact.
An introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry. One of the main motivations, and a major source of examples, is string theory, where orbifolds play an important role. The subject is first developed following the classical description analogous to manifold theory, after which the book branches out to include the useful description of orbifolds provided by groupoids, as well as many examples in the context of algebraic geometry. Classical invariants such as de Rham cohomology and bundle theory are developed, a careful study of orbifold morphisms is provided, and the topic of orbifold K-theory is covered. The heart of this book, however, is a detailed description of the Chen-Ruan cohomology, which introduces a product for orbifolds and has had significant impact. The final chapter includes explicit computations for a number of interesting examples.
Cohomology, Group Actions, and Topology : Summer Research Institute on Cohomology, Representations, and Actions of Finite Groups, July 7-27, 1996, University of Washington, Seattle
Cohomology, Group Actions, and Topology : Summer Research Institute on Cohomology, Representations, and Actions of Finite Groups, July 7-27, 1996, University of Washington, Seattle
This volume combines contributions in topology and representation theory that reflect the increasingly vigorous interactions between these areas. Topics such as group theory, homotopy theory, cohomology of groups, and modular representations are covered. All papers have been carefully refereed and offer lasting value.
Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homo logical algebra and algebraic K-theory. It arose primarily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work ofH. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the meanings of the low dimensional homology groups of a space X. For example, if the universal cover of X was three connected, it was known that H2(X; A. ) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N
This book is an excellent illustration of the versatility of Algebraic Topology interacting with other areas in Mathematics and Physics. Topics discussed in this volume range from classical Differential Topology and Homotopy Theory (Kervaire invariant one problem) to more recent lines of research such as Topological Quantum Field Theory (string theory). Likewise, alternative viewpoints on classical problems in Global Analysis and Dynamical Systems are developed (a spectral sequence approach to normal form theory). This collection of papers is based on talks at the conference on the occasion of Sam Gitler's 70th birthday (December, 2003). The variety of topics covered in this book reflects the many areas where Sam Gitler's contributions have had an impact.
This book is the result of a conference held to examine developments in homotopy theory in honor of Samuel Gitler in July 1993 (Cocoyoc, Mexico). It includes several research papers and three expository papers on various topics in homotopy theory. The research papers discuss the following: BL application of homotopy theory to group theory BL fiber bundle theory BL homotopy theory The expository papers consider the following topics: BL the Atiyah-Jones conjecture (by C. Boyer) BL classifying spaces of finite groups (by J. Martino) BL instanton moduli spaces (by J. Milgram) Homotopy Theory and Its Applications offers a distinctive account of how homotopy theoretic methods can be applied to a variety of interesting problems.
Many neurologic disorders can appear in quick and severe forms that require immediate medical attention. This issue of Neurologic Clinics features 14 articles on conditions that commonly present acutely, such as epilepsy, headache, visual loss, nervous system infections, ischemic stroke, head and spinal cord injury, and intracranial hemorrhage.
As a core part of the central nervous system, the spinal cord has a distinctive role in the etiology and exacerbation of common and less common neurologic disorders. This issue of Neurologic Clinics will look at the spinal cord’s involvement in disorders arising generally in the CNS, as well as disorders based within the cord itself. Articles include: Spinal cord: A review of functional neuroanatomy; Infections of spinal cord; Multiple sclerosis and spinal cord; Transverse myelitis; Neuromyelitis optica; Vascular disorders of spinal cord; Spine and spinal cord trauma; Imaging of spinal cord: General principles; Toxic, nutritional, and metabolic deficiencies of spinal cord; Spinal cord: Motor neuron diseases; Spinal cord tumors: New views and future directions; Spinal cord and spasticity: A mechanistic view; Cervical spondylosis and stenosis; Autonomic nervous system disorders and spinal cord; Stiff person syndrome: What is new?; Sleep disorders in patients with spinal cord injury.
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