String Topology and Cyclic Homology

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 presents material for a broader audience that was formerly available only to advanced specialists. In addition to presenting thorough exposition and practical models, the book offers as extensive references for further study.

List of contents

Notes on String Topology.- Intersection theory in loop spaces.- The cacti operad.- Field theoretic properties of string topology.- A Morse theoretic viewpoint.- Brane topology.- An Algebraic Model for Mod 2 Topological Cyclic Homology.- Preliminaries.- Free loop spaces.- Homotopy orbit spaces.- A model for mod 2 topological cyclic homology.

Summary

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 presents material for a broader audience that was formerly available only to advanced specialists. In addition to presenting thorough exposition and practical models, the book offers as extensive references for further study.

Additional text

From the reviews:
“This book gives an introduction to some exciting recent developments in the topology of free loop spaces. It should be a good starting point for a more detailed study of the rapidly developing literature on this subject, and given the pace of these advances, this maybe the best that could be hoped for.” (Janko Latschev, Bulletin of the American Mathematical Society, Vol. 47 (4), October, 2010)

Report

From the reviews:
"This book gives an introduction to some exciting recent developments in the topology of free loop spaces. It should be a good starting point for a more detailed study of the rapidly developing literature on this subject, and given the pace of these advances, this maybe the best that could be hoped for." (Janko Latschev, Bulletin of the American Mathematical Society, Vol. 47 (4), October, 2010)

Product details

• Authors: Ralph Cohen, Ralph L Cohen, Ralph L. Cohen, Kathry Hess, Kathryn Hess, Dennis Sullivan, Alexander A Voronov, Alexander A. Voronov
• Publisher: Springer, Basel
• Languages: English
• Product format: Paperback / Softback
• Released: 30.01.2006
• EAN: 9783764321826
• ISBN: 978-3-7643-2182-6
• No. of pages: 163
• Weight: 309 g
• Illustrations: VII, 163 p.
• Series: Advanced Courses in Mathematics - CRM Barcelona; Advanced Courses in Mathematics CRM Barcelona; Advanced Courses in Mathematics - CRM Barcelona
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; B, Physics, Mathematics and Statistics, Mathematical physics, Manifolds and Cell Complexes (incl. Diff.Topology), Manifolds (Mathematics), Analytic geometry, Manifolds and Cell Complexes, Complex manifolds, Analytic topology, Mathematical Methods in Physics, Algebraic Topology