English

Exact triangles in monopole homology and the Casson-Walker invariant

Geometric Topology 2007-05-23 v1

Abstract

We establish the exact triangle in Seiberg-Witten-Floer theory relating the monopoloe homologies of any two closed 3-manifolds which are obtained from each other by ±1\pm 1-surgery. We also show that the sum of the modified version of the Seiberg-Witten invariants for any closed rational homology 3-sphere YY over all SpincSpin^c structures equals to 12H1(Y,Z)λ(Y)\frac 12 |H_1(Y, \Z)| \lambda (Y) where λ(Y)\lambda (Y) is the Casson-Walker invariant.

Keywords

Cite

@article{arxiv.math/0101127,
  title  = {Exact triangles in monopole homology and the Casson-Walker invariant},
  author = {Matilde Marcolli and Bai-Ling Wang},
  journal= {arXiv preprint arXiv:math/0101127},
  year   = {2007}
}

Comments

35 pages, 3 figures