Virtual Fundamental Cycles in Symplectic Topology
About this Title
Dusa McDuff, Columbia University, New York, NY, Mohammad Tehrani, University of Iowa, Iowa City, IA, Kenji Fukaya, Simons Center for Geometry and Physics, Stony Brook, NY and Dominic Joyce, Mathematical Institute, Oxford, United Kingdom. Edited by John W. Morgan, Simons Center for Geometry and Physics, Stony Brook, NY
Publication: Mathematical Surveys and Monographs
Publication Year: 2019; Volume 237
ISBNs: 978-1-4704-5014-4 (print); 978-1-4704-5202-5 (online)
MathSciNet review: 3929752
MSC: Primary 53D45; Secondary 53D37, 57R17, 57R18, 58J10
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.
Graduate students and researchers interested in recent developments in symplectic topology and moduli spaces.
Table of Contents
- Notes on Kuranishi atlases
- Gromov-Witten theory via Kuranishi structures
- Kuranishi spaces as a 2-category