Virtual fundamental cycles in symplectic topology / John W. Morgan, editor ; Dusa McDuff, Mohammad Tehrani, Kenji Fukaya, Dominic Joyce.

Format:

Book

Author/Creator:

McDuff, Dusa, 1945- author.

Tehrani, Mohammad, author.

Fukaya, Kenji, 1959- author.

Joyce, Dominic D., author.

Contributor:

Morgan, John, 1946 March 21- editor.

Simons Center for Geometry and Physics (Stony Brook University), issuing body, publisher.

Series:

Mathematical surveys and monographs ; no. 237.

Mathematical surveys and monographs ; volume 237

Language:

English

Subjects (All):

Symplectic geometry.

Geometry, Differential.

Differential geometry--Symplectic geometry, contact geometry--Gromov-Witten invariants, quantum cohomology, Frobenius manifolds.

Differential geometry--Symplectic geometry, contact geometry--Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category.

Global analysis, analysis on manifolds--Partial differential equations on manifolds; differential operators--Differential complexes.

Manifolds and cell complexes--Differential topology--Symplectic and contact topology.

Manifolds and cell complexes--Differential topology--Topology and geometry of orbifolds.

Local Subjects:

Differential geometry--Symplectic geometry, contact geometry--Gromov-Witten invariants, quantum cohomology, Frobenius manifolds.

Differential geometry--Symplectic geometry, contact geometry--Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category.

Global analysis, analysis on manifolds--Partial differential equations on manifolds; differential operators--Differential complexes.

Manifolds and cell complexes--Differential topology--Symplectic and contact topology.

Manifolds and cell complexes--Differential topology--Topology and geometry of orbifolds.

Geometry, Differential.

Symplectic geometry.

Physical Description:

xv, 298 pages : illustrations ; 27 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society ; [Stony Brook, New York] : Simons Center for Geometry and Physics, [2019]

Summary:

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.

Contents:

Introduction / by John W. Morgan

Notes on Kuranishi atlases / by Dusa McDuff

Gromov-Witten theory via Kuranishi structures / by Mohammad F. Tehrani and Kenji Fukaya

Kuranishi spaces as a 2-category / by Dominic Joyce.

Notes:

Includes bibliographical references.

ISBN:

9781470450144

1470450143

OCLC:

1080251406