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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

A symplectic prolegomenon


Author: Ivan Smith
Journal: Bull. Amer. Math. Soc. 52 (2015), 415-464
MSC (2010): Primary 53D35, 53D40, 53D37
DOI: https://doi.org/10.1090/S0273-0979-2015-01477-1
Published electronically: January 30, 2015
MathSciNet review: 3348443
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Abstract: A symplectic manifold gives rise to a triangulated $ A_{\infty }$-category, the derived Fukaya category, which encodes information on Lagrangian submanifolds and dynamics as probed by Floer cohomology. This survey aims to give some insight into what the Fukaya category is, where it comes from, and what symplectic topologists want to do with it.


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Additional Information

Ivan Smith
Affiliation: Centre for Mathematical Sciences, University of Cambridge, CB3 0WB, England.
Email: is200@cam.ac.uk

DOI: https://doi.org/10.1090/S0273-0979-2015-01477-1
Received by editor(s) in revised form: January 2, 2014
Published electronically: January 30, 2015
Article copyright: © Copyright 2015 American Mathematical Society