A Perturbative SU(3) Casson Invariant

S. E. Cappell; R. Lee; E. Y. Miller

A Perturbative SU(3) Casson Invariant

微分几何 2007-05-23 v1 几何拓扑

作者: S. E. Cappell , R. Lee , E. Y. Miller

摘要

A perturbative SU(3) Casson invariant $\Lambda_{SU(3)}(X)$ for integral homology 3-spheres is defined. Besides being fully perturbative, it has nice properties: (1) $4 . \Lambda_{SU(3)}(X)$ is an integer. (2) It is preseved under orientation change. (3) A connected sum formula holds. Explicit calculations of the invariant for $1/k$ surgery on $(2,q)$ torus knots are made and compared with a different generalization of Casson's invariant to SU(3) by Boden and Herald. For those cases computed, the invariant defined here is a quadratic polynomial in k for k>0 and a quadratic polynomial for k<0.

关键词

seiberg-witten invariants knot invariants dehn surgery

引用

@article{arxiv.math/0006018,
  title  = {A Perturbative SU(3) Casson Invariant},
  author = {S. E. Cappell and R. Lee and E. Y. Miller},
  journal= {arXiv preprint arXiv:math/0006018},
  year   = {2007}
}

备注

39 pages, 4 tables

A Perturbative SU(3) Casson Invariant

摘要

关键词

引用

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