Symplectic cohomology of compound Du Val singularities
Annales Henri Lebesgue, Volume 6 (2023), pp. 727-765.


Keywords Symplectic cohomology, compound Du Val, terminal, singularities, contact geometry, links, homological mirror symmetry


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 .


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