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.

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.

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. The book provides many references for the reader wishing to learn more about the subject, to which it gives a perfect introduction. It is therefore suitable for both graduate students and established researchers. It is certainly the best source of much information that was until now available only to specialists and covers material from the elementary bases to the most recent developments.

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)

Provides many references for the reader wishing to learn more about the subject Gives a perfect introduction to this subject and is therefore suitable for graduate students and confirmed researchers Best place to find many informations which were up to now only available to specialists Covers material from the elementary bases to the most recent developments Includes supplementary material: sn.pub/extras