The Seiberg–Witten invariant conjecture for constants of nice surface singularities

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Let XX be a nice normal surface singularity with rational homology sphere link MM, and let HH index the constants \\{\mathrm{const}_h\}_{h\in H}. The group HH acts on the set of spin⁡c\operatorname{spin}^c-structures of MM, and \textsigmacan\textsigma_{\mathrm{can}} denotes the canonical spin⁡c\operatorname{spin}^c-structure induced by the complex structure of XX.

Seiberg–Witten invariant conjecture. The constants are the Seiberg–Witten invariants of the link, namely

consth=sw⁡h∗\textsigmacan.\mathrm{const}_h=\operatorname{sw}_{h*\textsigma_{\mathrm{can}}}.

This is presented as a reinterpretation of the Seiberg–Witten Invariant Conjecture for the constants appearing in the cohomology formula for line bundles. The supplied text does not state whether the conjecture has been proved or disproved.

References

Primary source

András Némethi, “The cohomology of line bundles of splice-quotient singularities”, arXiv:0810.4129 (2008).

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