# 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.

#### Readership

Graduate students interested in free loop spaces.