Open AccessThe geometric genus, the casson invariant conjecture and splice type singularities
Author(s) -
Tomohiro Okuma
Publication year - 2010
Publication title -
demonstratio mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.541
H-Index - 28
eISSN - 2391-4661
pISSN - 0420-1213
DOI - 10.1515/dema-2013-0247
Subject(s) - mathematics , gravitational singularity , quotient , singularity , conjecture , invariant (physics) , normal surface , pure mathematics , homology (biology) , isolated singularity , topology (electrical circuits) , combinatorics , surface (topology) , mathematical analysis , geometry , mathematical physics , biochemistry , chemistry , gene
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.