Symplectic cohomology of compound Du Val singularities

Jonathan David Evans; Yanki Lekili

Symplectic cohomology of compound Du Val singularities

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arxiv 2104.11713 v3 pith:XQDP22ET submitted 2021-04-23 math.SG math.AGmath.GT

Jonathan David Evans , Yanki Lekili This is my paper · ORCID

classification math.SGmath.AGmath.GT

keywords cohomologysingularitiessymplecticcompoundcomputationscontactresolutionsmall

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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 $S^2 \times S^3$.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

On holographic duals of certain isolated weighted Gorenstein cDV singularities
hep-th 2024-12 reject novelty 5.0 of 10

The paper claims, via mirror symmetry and a quiver search, that none of a listed set of cE6 and cE7 singularities admit crepant resolutions and hence lack N=1 quiver SCFT duals.

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