Journal of Symplectic Geometry

Volume 19 (2021)

Number 5

Squared Dehn twists and deformed symplectic invariants

Pages: 1189 – 1280



Kyler Siegel (Department of Mathematics, University of Southern California, Los Angeles, Cal., U.S.A.)


We establish an infinitesimal version of fragility for squared Dehn twists around even dimensional Lagrangian spheres. The precise formulation involves twisting the Fukaya category by a closed two-form or bulk deforming it by a half-dimensional cycle. As our main application, we compute the twisted and bulk deformed symplectic cohomology of the subflexible Weinstein manifolds constructed in [27].

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The author was partially supported by NSF grant DGE-114747.

Received 1 December 2016

Accepted 24 January 2021

Published 27 May 2022