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The closed-open string
map for $S^1$–invariant Lagrangians
Dmitry Tonkonog |
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Algebraic & Geometric Topology 18 (2018) 15–68
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Abstract |
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Given a monotone Lagrangian submanifold invariant under a loop of Hamiltonian diffeomorphisms, we compute a piece of the closed-open string map into the Hochschild cohomology of the Lagrangian which captures the homology class of the loop’s orbit. Our applications include split-generation and nonformality results for real Lagrangians in projective spaces and other toric varieties; a particularly basic example is that the equatorial circle on the –sphere carries a nonformal Fukaya algebra in characteristic . |
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Keywords
circle action, Lagrangian submanifold, Floer homology,
closed-open map, Fukaya category, split-generation,
formality
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Mathematical Subject Classification 2010
Primary: 53D37, 53D40, 57R58
Secondary: 53D45
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References |
Publication
Received: 8 April 2015
Revised: 19 May 2017
Accepted: 11 June 2017
Published: 10 January 2018
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Authors |
| Dmitry Tonkonog | |
| Department of Pure Mathematics and
Mathematical Statistics University of Cambridge Cambridge United Kingdom |
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