Virtual Fundamental Cycles in Symplectic Topology
Seiten
2019
American Mathematical Society (Verlag)
978-1-4704-5014-4 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-5014-4 (ISBN)
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. The book offers a comprehensive understanding of the details of these constructions and the assumptions under which they can be made.
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 Simons Center for Geometry and Physics.
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 Simons Center for Geometry and Physics.
John W. Morgan, Simons Center for Geometry and Physics, Stony Brook, NY.
D. McDuff, Notes on Kuranishi atlases
M. F. Tehrani and K. Fukaya, Gromov-Witten theory via Kuranishi structures
D. Joyce, Kuranishi spaces as a 2-category
| Erscheinungsdatum | 02.05.2019 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 755 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-4704-5014-3 / 1470450143 |
| ISBN-13 | 978-1-4704-5014-4 / 9781470450144 |
| Zustand | Neuware |
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