Synopses & Reviews
Review
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)
Synopsis
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. The second gives a complete and clear construction of an algebraic model for computing topological cyclic homology.
Synopsis
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.
Synopsis
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.
Synopsis
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.
Table of Contents
Foreword.- Notes on String Topology (R.L. Cohen and A.A. Voronov) - Introduction.- Intersection Theory in Loop Spaces - The Cacti Operad - String Topology as Field Theory - A Morse Theoretic Viewpoint - Brane Topology - Bibliography.- An Algebraic Model for Mod 2 Topological Cyclic Homology (K. Hess) - Preface - Preliminaries - Free Loop Spaces - Homotopy Orbit Spaces - A Model for Mod 2 Toplological Cyclic Homology - Bibliography.