The symplectic geometry of cotangent bundles from a categorical viewpoint

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We describe various approaches to understanding Fukaya categories of cotangent bundles. All of the approaches rely on introducing a suitable class of noncompact Lagrangian submanifolds. We review the work of Nadler-Zaslow (math/0604379, math/0612399) and the authors (math/0701783), before discussing a new approach using family Floer cohomology and the ``wrapped Fukaya category''. The latter, inspired by Viterbo's symplectic homology, emphasises the connection to loop spaces, hence seems particularly suitable when trying to extend the existing theory beyond the simply-connected case.
27 pages, 2 figures. Version 4 -- application added (to exact Lagrangians in Euclidean space which are standard at infinity), results sharpened for cotangent bundles of tori

Keywords

Symplectic Geometry, Algebraic Topology, 53D35; 53D40; 57T30

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/138653

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0705.3450
 http://arxiv.org/abs/0705.3450

Collections

arXiv