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Virtual Fundamental Cycles in Symplectic Topology
 
Dusa McDuff Columbia University, New York, NY
Edited by: John W. Morgan Simons Center for Geometry and Physics, Stony Brook, NY
Mohammad Tehrani University of Iowa, Iowa City, IA
Kenji Fukaya Simons Center for Geometry and Physics, Stony Brook, NY
Dominic Joyce Mathematical Institute, Oxford, United Kingdom
Virtual Fundamental Cycles in Symplectic Topology
Hardcover ISBN:  978-1-4704-5014-4
Product Code:  SURV/237
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-5202-5
Product Code:  SURV/237.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-1-4704-5014-4
eBook: ISBN:  978-1-4704-5202-5
Product Code:  SURV/237.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Virtual Fundamental Cycles in Symplectic Topology
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Virtual Fundamental Cycles in Symplectic Topology
Dusa McDuff Columbia University, New York, NY
Edited by: John W. Morgan Simons Center for Geometry and Physics, Stony Brook, NY
Mohammad Tehrani University of Iowa, Iowa City, IA
Kenji Fukaya Simons Center for Geometry and Physics, Stony Brook, NY
Dominic Joyce Mathematical Institute, Oxford, United Kingdom
Hardcover ISBN:  978-1-4704-5014-4
Product Code:  SURV/237
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-5202-5
Product Code:  SURV/237.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-1-4704-5014-4
eBook ISBN:  978-1-4704-5202-5
Product Code:  SURV/237.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2372019; 300 pp
    MSC: Primary 53; 58; 57

    The method of using the moduli space of pseudo-holomorphic curves on a symplectic manifold was introduced by Mikhail Gromov in 1985. From the appearance of Gromov's original paper until today this approach has been the most important tool in global symplectic geometry. To produce numerical invariants of these manifolds using this method requires constructing a fundamental cycle associated with moduli spaces.

    This volume brings together three approaches to constructing the “virtual” fundamental cycle for the moduli space of pseudo-holomorphic curves. All approaches are based on the idea of local Kuranishi charts for the moduli space. Workers in the field will get a comprehensive understanding of the details of these constructions and the assumptions under which they can be made. These techniques and results will be essential in further applications of this approach to producing invariants of symplectic manifolds.

    This book is published in cooperation with the Simons Center for Geometry and Physics.
    Readership

    Graduate students and researchers interested in recent developments in symplectic topology and moduli spaces.

  • Table of Contents
     
     
    • Chapters
    • Notes on Kuranishi atlases
    • Gromov-Witten theory via Kuranishi structures
    • Kuranishi spaces as a 2-category
  • Reviews
     
     
    • This book covers relatively new material in the area and expands symplectic topology in a unique way while assisting with a better understanding of the basics of the theory of virtual fundamental chain and cycle. Second, it contains many well-explained relevant examples. Finally, all three chapters complement each other yet can be studied individually.

      Filiz Dogru, MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2372019; 300 pp
MSC: Primary 53; 58; 57

The method of using the moduli space of pseudo-holomorphic curves on a symplectic manifold was introduced by Mikhail Gromov in 1985. From the appearance of Gromov's original paper until today this approach has been the most important tool in global symplectic geometry. To produce numerical invariants of these manifolds using this method requires constructing a fundamental cycle associated with moduli spaces.

This volume brings together three approaches to constructing the “virtual” fundamental cycle for the moduli space of pseudo-holomorphic curves. All approaches are based on the idea of local Kuranishi charts for the moduli space. Workers in the field will get a comprehensive understanding of the details of these constructions and the assumptions under which they can be made. These techniques and results will be essential in further applications of this approach to producing invariants of symplectic manifolds.

This book is published in cooperation with the Simons Center for Geometry and Physics.
Readership

Graduate students and researchers interested in recent developments in symplectic topology and moduli spaces.

  • Chapters
  • Notes on Kuranishi atlases
  • Gromov-Witten theory via Kuranishi structures
  • Kuranishi spaces as a 2-category
  • This book covers relatively new material in the area and expands symplectic topology in a unique way while assisting with a better understanding of the basics of the theory of virtual fundamental chain and cycle. Second, it contains many well-explained relevant examples. Finally, all three chapters complement each other yet can be studied individually.

    Filiz Dogru, MAA Reviews
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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