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2019 Topology of (small) Lagrangian cobordisms
Mads R Bisgaard
Algebr. Geom. Topol. 19(2): 701-742 (2019). DOI: 10.2140/agt.2019.19.701

Abstract

We study the following quantitative phenomenon in symplectic topology: in many situations, if a Lagrangian cobordism is sufficiently small (in a sense we specify) then its topology is to a large extend determined by its boundary. This principle allows us to derive several homological uniqueness results for small Lagrangian cobordisms. In particular, under the smallness assumption, we prove homological uniqueness of the class of Lagrangian cobordisms, which, by Biran and Cornea’s Lagrangian cobordism theory, induces operations on a version of the derived Fukaya category. We also establish a link between our results and Vassilyev’s theory of Lagrange characteristic classes. Most currently known constructions of Lagrangian cobordisms yield small Lagrangian cobordisms in many examples.

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Mads R Bisgaard. "Topology of (small) Lagrangian cobordisms." Algebr. Geom. Topol. 19 (2) 701 - 742, 2019. https://doi.org/10.2140/agt.2019.19.701

Information

Received: 8 August 2017; Revised: 26 June 2018; Accepted: 14 August 2018; Published: 2019
First available in Project Euclid: 19 March 2019

zbMATH: 07075113
MathSciNet: MR3924176
Digital Object Identifier: 10.2140/agt.2019.19.701

Subjects:
Primary: 53D05, 53D12, 53D40

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 2 • 2019
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