Symplectic cohomology of compound Du Val singularities

Evans, Jonny and Lekili, YankI (2022) Symplectic cohomology of compound Du Val singularities. Annales Henri Lebesgue. ISSN 2644-9463 (In Press)

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Abstract

We compute symplectic cohomology for Milnor fibres of certain compound Du Val singularities that admit small resolution by using homological mirror symmetry. Our computations suggest a new conjecture that the existence of a small resolution has strong implications for the symplectic cohomology and conversely. We also use our computations to give a contact invariant of the link of the singularities and thereby distinguish many contact structures on connected sums of S^2×S^3.