Symplectic cohomology of compound Du Val singularities

Evans, Jonathan David; Lekili, Yankı

Annales Henri Lebesgue, Tome 6 (2023), pp. 727-765

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 $S^2\times S^3$.

Nous calculons la cohomologie symplectique des fibres de Milnor de certaines singularités Du Val composites qui admettent une petite résolution en utilisant la symétrie miroir homologique. Nos calculs suggèrent une nouvelle conjecture comme quoi l’existence d’une petite résolution a de fortes implications pour la cohomologie symplectique et inversement. Nous utilisons également nos calculs pour donner un invariant de contact du link des singularités et ainsi distinguer de nombreuses structures de contact sur des sommes connexes de $S^2\times S^3$.

Classification : 53D35, 53D37, 53D40
Keywords: Symplectic cohomology, compound Du Val, terminal, singularities, contact geometry, links, homological mirror symmetry

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