**EMS IRMA Lectures in Mathematics and Theoretical Physics**

Volume: 24;
2015;
500 pp;
Hardcover

MSC: Primary 53; 55; 13; 16;
Secondary 57

**Print ISBN: 978-3-03719-153-8
Product Code: EMSILMTP/24**

List Price: $87.00

Individual Member Price: $69.60

# Free Loop Spaces in Geometry and Topology: Including the Monograph "Symplectic Cohomology and Viterbo’s Theorem"

Share this page *Edited by *
*Janko Latschev; Alexandru Oancea*

A publication of the European Mathematical Society

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 who approach the topic from both perspectives and provides a concise overview of many of the classical results. The book also begins to explore the new directions of research that have emerged recently. One highlight is the research monograph by M. Abouzaid, which proves a strengthened version of Viterbo's 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 graduate students 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.

A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.

#### Table of Contents

# Table of Contents

## Free Loop Spaces in Geometry and Topology: Including the Monograph "Symplectic Cohomology and Viterbo's Theorem"

#### Readership

Graduate students interested in free loop spaces.