Some speculations on pairs-of-pants decompositions and Fukaya categories
Name
1004.0906.pdf
Size
228.8 KB
Format
Adobe PDF
Checksum (MD5)
2de22f26c9f4283898ab37d24d4664e3
Author(s)
Seidel, Paul Alfred
Date Issued
2012
Journal
Surveys in Differential Geometry
Publisher
International Press of Boston
Citation
Seidel, Paul. “Some Speculations on Pairs-of-Pants Decompositions and Fukaya Categories.” Surveys in Differential Geometry 17, 1 (2012): 411–426 © 2012 International Press of Boston
Version
Original manuscript
Abstract
This is partly a survey and partly a speculative article, concerning a
particular question about Fukaya categories of symplectic manifolds.
Namely, can we decompose a symplectic manifold into standard pieces, and then reconstruct its Fukaya category by gluing together categories depending only on the geometry of each piece, in a (loosely understood) sheaf-theoretic way? For this to work, some degree of control over pseudo-holomorphic curves is required, an issue which depends on the geometry of the decomposition under consideration. Sheaf-theoretic ideas have been successfully applied to the symplectic geometry of cotangent bundles, starting with the work of Fukaya-Oh [17], and followed by Kasturirangan-Oh [26, 39] and Nadler-Zaslow [35,36] (for a survey of the last-mentioned work and related ideas of Fukaya-Smith, see [19]). Recently, Kontsevich [28] has proposed a generalization to Stein manifolds whose Lagrangian skeleta have certain singularities. However, that is not quite the direction we wish to take here.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4310/SDG.2012.V17.N1.A9
