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The geometric genus, the Casson invariant conjecture and splice type singularities

Okuma T.

Demonstratio Mathematica

2010

Vol. 43, nr 2

325-338

This is a survey of some results on splice-quotient singularities which are a natural and broad generalization of quasihomogeneous surface singularities with rational homology sphere links. From its topology (i.e., the link or the resolution graph), we can write down the "leading terms" of equations of a splice-quotient singularity, and compute the geometric genus. Applying the formula for the geometric genus, we can verify the Casson invariant conjecture for splice-quotient singularities.