Surgery formula for Seiberg--Witten invariants of negative definite plumbed 3-manifolds

Details Surgery formula for Seiberg--Witten invariants of negative definite plumbed 3-manifolds Surgery formula for Seiberg--Witten invariants of negative definite plumbed 3-manifolds

2007-04-24

arxiv.org/abs/0704.3145v2

Mathematics

Geometric Topology

17 pages, 4 figures, accepted by Journal f\"ur die reine und angewandte Mathematik. Minor improvements suggested by referee

Scientific paper

We derive a cut-and-paste surgery formula of Seiberg--Witten invariants for negative definite plumbed rational homology 3-spheres. It is similar to (and motivated by) Okuma's recursion formula [arXiv:math.AG/0610464, 4.5] targeting analytic invariants of splice quotient singularities. The two formulas combined provide automatically a proof of the equivariant version [arXiv:math.AG/0310084, 5.2(b)] of the `Seiberg--Witten invariant conjecture' [arXiv:math.AG/0111298] for these singularities.

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