Topology of (small) Lagrangian cobordisms

Bisgaard, Mads

doi:10.2140/agt.2019.19.701

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Topology of (small) Lagrangian cobordisms

Mads R Bisgaard

Algebraic & Geometric Topology 19 (2019) 701–742

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.

Keywords

Lagrangian cobordisms, Floer homology, Lagrangian submanifolds

Mathematical Subject Classification 2010

Primary: 53D05, 53D12, 53D40

References

Publication

Received: 8 August 2017

Revised: 26 June 2018

Accepted: 14 August 2018

Published: 12 March 2019

Authors

Mads R Bisgaard
Department of Mathematics ETH Zürich Zurich Switzerland

Volume 19, issue 2 (2019)