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Journal of the London Mathematical Society Advance Access published online on April 24, 2008
Journal of the London Mathematical Society, doi:10.1112/jlms/jdn020
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© 2008 London Mathematical Society

The Seiberg–Witten invariant conjecture for splice-quotients

András Némethi

Rényi Institute of Mathematics
Budapest
Hungary
nemethi@renyi.hu

Tomohiro Okuma

Department of Education
Yamagata University
Yamagata 990-8560
Japan

Splice-quotient singularities were introduced recently and studied intensively by Neumann and Wahl. For such a singularity we prove that the geometric genus can be recovered from the topology of the singularity, namely from the Seiberg–Witten invariant (associated with the canonical spinc structure) of the link. This answers positively the conjecture formulated by the first author and Nicolaescu.

The first author is partially supported by a Marie Curie grant and OTKA grants, and the second author by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports, Science and Technology, Japan.

2000 Mathematics Subject Classification 14B05, 14J17, 32S25, 57M27, 57R57 (primary), 14E15, 32S45, 57M25 (secondary).

Received January 9, 2007; revised February 5, 2008;
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