The symplectic geometry of cotangent bundles from a categorical viewpoint

2007/05/23 by Kenji Fukaya, Paul Seidel, Fukaya, Kenji +3 · 4 citations
Mathematics · Medicine · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Botulinum Toxin and Related Neurological Disorders

paper · pdf · doi:10.48550/arxiv.0705.3450

Abstract

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.

Cited by

• Hochschild Cohomology of the Symmetric Square of an Annulus with Stops
• Floer homology on the universal cover, a proof of Audin's conjecture and\n other constraints on Lagrangian submanifolds
• Lagrangian Floer theory, from geometry to algebra and back again
• Complexifications of Morse functions and the directed Donaldson-Fukaya category

Related

• A cotangent fibre generates the Fukaya category
• A beginner's introduction to Fukaya categories
• A symplectic prolegomenon
• Symplectic cohomology and duality for the wrapped Fukaya category
• Functoriality in categorical symplectic geometry