Neumann–Wahl Casson invariant conjecture

Let (X,o)(X,o) be a complete intersection isolated surface singularity, and let its link (X,o)\partial(X,o) be an integral homology sphere.

Casson invariant conjecture. The Casson invariant of (X,o)\partial(X,o) is equal to one-eighth of the signature of the Milnor fiber of (X,o)(X,o).

This conjecture concerns the relationship between the topology of links of complete intersection surface singularities and the topology of their Milnor fibers. It was later proved for splice type singularities with integral homology sphere links by Némethi and Okuma.

Sources & referencesView supporting material

Primary source

Maria Angelica Cueto, Patrick Popescu-Pampu and Dmitry Stepanov, “The Milnor fiber conjecture of Neumann and Wahl, and an overview of its proof”, arXiv:2205.12839 (2022).

Additional references

3 papers in this index state this conjecture (2005–2022). The statement above is taken from the most recent of them; the others are arXiv:1310.1268, arXiv:math/0509085.

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