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String topology and cyclic homology

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Published by Birkhäuser Verlag in Boston .
Written in English

Subjects:

  • Loop spaces.,
  • Homotopy theory.,
  • Complex manifolds.,
  • Differential topology.,
  • Algebraic topology.

Book details:

Edition Notes

Includes bibliographical references.

StatementRalph L. Cohen, Kathryn Hess, Alexander A. Voronov.
SeriesAdvanced courses in mathematics, CRM Barcelona
ContributionsHess, Kathryn, 1967-, Voronov, Alexander A.
Classifications
LC ClassificationsQA612.76 .C64 2006
The Physical Object
Paginationp. cm.
ID Numbers
Open LibraryOL3432442M
ISBN 103764321822, 3764373881
ISBN 109783764321826
LC Control Number2005058913

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This book explores string topology, Hochschild and cyclic homology, assembling material from a wide scattering of scholarly sources in a single practical volume. The text string topology from the elementary bases to the most recent developments, presenting material for a broader audience that was formerly available only to advanced specialists. String Topology and Cyclic Homology.   Applications of the theory to string topology and the Fukaya category are given; in particular, it is shown that there is a Lie bialgebra homomorphism from the cyclic cohomology of the Fukaya category of a symplectic manifold with contact type boundary to the linearized contact homology Cited by: 5. Notes on String Topology. String topology is the study of algebraic and differential topological properties of spaces of paths and loops in manifolds. Topics covered includes: Intersection theory in loop spaces, The cacti operad, String topology as field theory, A Morse theoretic viewpoint, Brane topology.

String topology, a branch of mathematics, is the study of algebraic structures on the homology of free loop spaces. The field was started by Moira Chas and Dennis Sullivan. Contents Foreword vii I Notes on String Topology Ralph L. Cohen and Alexander A. Voronov 1 Introduction 3 1 Intersectiontheoryinloopspaces 5 Summary: The subject of this book is string topology, Hochschild and cyclic homology. The first part consists of an excellent exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clear construction of an algebraic model for computing topological cyclic homology. String Topology and the Hochschild like ranks of cyclic homology groups, are expected to be given by `matrix integrals' over representation varieties. In string perturbation theory.

The construction of topological cyclic homology is based on genuine equivariant homotopy theory, the use of explicit point-set models, and the elaborate notion of a cyclotomic spectrum. The goal of this paper is to revisit this theory using only homotopy-invariant notions. In particular, we give a new construction of topological cyclic by: given at the Summer School on String Topology and Hochschild Homology, in Almer´ıa, Spain. In our view there are two basic reasons for the excitement about the develop-ment of string topology. First, it uses most of the modern techniques of algebraic topology, and relates them to several other areas of mathematics. For example,File Size: KB. Buy (ebook) String Topology and Cyclic Homology by Ralph L. Cohen, Alexander A. Voronov, Kathryn Hess, eBook format, from the Dymocks online bookstore. This book explores string topology, Hochschild and cyclic homology, assembling material from a wide scattering of scholarly sources in a single practical volume. The first part offers a thorough and elegant exposition of various approaches to string topology and the Chas-Sullivan loop product.