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

Edited by: Janko Latschev University of Hamburg, Germany
Alexandru Oancea Sorbonne Universités, Paris, France
A publication of European Mathematical Society
Available Formats:
Hardcover ISBN: 978-3-03719-153-8
Product Code: EMSILMTP/24
List Price: $87.00 AMS Member Price:$69.60
Please note AMS points can not be used for this product
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Free Loop Spaces in Geometry and Topology: Including the Monograph "Symplectic Cohomology and Viterbo’s Theorem"
Edited by: Janko Latschev University of Hamburg, Germany
Alexandru Oancea Sorbonne Universités, Paris, France
A publication of European Mathematical Society
Available Formats:
 Hardcover ISBN: 978-3-03719-153-8 Product Code: EMSILMTP/24
 List Price: $87.00 AMS Member Price:$69.60
Please note AMS points can not be used for this product
• Book Details

EMS IRMA Lectures in Mathematics and Theoretical Physics
Volume: 242015; 500 pp
MSC: Primary 53; 55; 13;

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.

Graduate students interested in free loop spaces.

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Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 242015; 500 pp
MSC: Primary 53; 55; 13;

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.