Free Loop Spaces in Geometry and Topology ; Including the monograph Symplectic cohomology and Viterbos theorem by Mohammed Abouzaid.

Format:

Book

Author/Creator:

Latschev, Editor.

Oancea, Alexandru, author.

Series:

IRMA Lectures in Mathematics and Theoretical Physics (irma) 2523-5141 24

Language:

English

Physical Description:

1 online resource (500 pages)

Place of Publication:

EMS Press 2015

System Details:

text file PDF

Summary:

In the late 1990s two initially unrelated developments brought free loop spaces into renewed focus. In 1999, Chas and Sullivan introduced a wealth of new algebraic operations on the homology of these spaces under the name of _string topology_, the full scope of which is still not completely understood. A few years earlier, Viterbo had discovered a first deep link between the _symplectic topology_ of cotangent bundles and the topology of their free loop space. In the past 15 years, many exciting connections between these two viewpoints have been found. Still, researchers working on one side of the story often know quite little about the other. One of the main purposes of this book is to facilitate communication between topologists and symplectic geometers thinking about free loop spaces. It was written by active researchers coming to the topic from both perspectives and provides a concise overview of many of the classical results, while also beginning to explore the new directions of research that have emerged recently. As one highlight, it contains a research monograph by M. Abouzaid which proves a strengthened version of Viterbos isomorphism between the homology of the free loop space of a manifold and the symplectic cohomology of its cotangent bundle, following a new strategy. The book grew out of a learning seminar on free loop spaces held at Strasbourg University in 2008-2009, and should be accessible to a graduate student with a general interest in the topic. It focuses on introducing and explaining the most important aspects rather than offering encyclopedic coverage, while providing the interested reader with a broad basis for further studies and research.

ISBN:

3-03719-653-X