Continuous and coherent actions on wrapped Fukaya categories

2019/11/01 by Oh, Yong-Geun, Tanaka, Hiro Lee · 3 citations
#Algebraic Topology (math.AT) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1911.00349

Abstract

We establish the continuous functoriality of wrapped Fukaya categories with respect to Liouville automorphisms, yielding a way to probe the homotopy type of the automorphism group of a Liouville sector. These methods prove Liouville and monotone cases of a conjecture of Teleman from the 2014 ICM. In the case of a cotangent bundle, we show that the Abouzaid equivalence between the wrapped category and the infinity-category of local systems intertwines our action with the action of diffeomorphisms of the zero section. In particular, our methods yield a typically non-trivial map from the rational homotopy groups of Liouville automorphisms to the rational string topology algebra of the zero section.

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• Plumbings of lens spaces and crepant resolutions of compound A_n singularities
• Semi-orthogonality in Fukaya-Seidel mirrors to blowups of abelian varieties
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