The Casson invariant conjecture

Let (X,0)(X,0) be the link of a hypersurface or complete intersection singularity, and let a3a3 be its integral homology-sphere link.

Casson invariant conjecture. The Casson invariant of a3a3 equals one-eighth the signature of the Milnor fiber.

This conjecture was described as a wildly optimistic assertion concerning links of hypersurface and complete intersection singularities. It is known for singularities of splice type, but the source does not establish it in full generality.

Sources & referencesView supporting material

Primary source

Jonathan Wahl, “Splice diagrams and splice-quotient surface singularities”, arXiv:2202.00587 (2022).

Additional references

2 papers in this index state this conjecture (2013–2022). The statement above is taken from the most recent of them; the others are arXiv:1305.0602.

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