Geodesic
Topology of (small) Lagrangian cobordisms
Bisgaard, Mads1
1 Department of Mathematics, ETH Zürich, Zurich, Switzerland
Algebraic and Geometric Topology, Tome 19 (2019) no. 2, pp. 701-742

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2019.19.701
Classification : 53D05, 53D12, 53D40
Keywords: Lagrangian cobordisms, Floer homology, Lagrangian submanifolds

Bisgaard, Mads 1

1 Department of Mathematics, ETH Zürich, Zurich, Switzerland 
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Bisgaard, Mads. Topology of (small) Lagrangian cobordisms. Algebraic and Geometric Topology, Tome 19 (2019) no. 2, pp. 701-742. doi: 10.2140/agt.2019.19.701

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