A perturbative SU(3) Casson invariant

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

Research output: Contribution to journalArticle

Abstract

A perturbative SU(3) Casson invariant ΛASU (X) for integral homology 3-sphere is defined. Besides being fully perturbative, it has the nice properties: (1) 4 · ΛSU(3) is an integer. (2) It is preserved under orientation change. (3) A connect sum formula. Explicit calculations of the invariant for 1/k surgery of (2, q) torus knot are presented and compared with Boden-Herald'S different SU(3) generalization of Casson'S invariant. For those cases computed, the invariant defined here is a quadratic polynomial in k; for k > 0 and a different quadratic polynomial for k < 0.

Original languageEnglish (US)
Pages (from-to)491-523
Number of pages33
JournalCommentarii Mathematici Helvetici
Volume77
Issue number3
DOIs
StatePublished - 2002

Keywords

  • Chern-Simons
  • Eta invariant
  • Floer homology
  • Gauge theory
  • Heegard decomposition
  • Index theory
  • Malsov index
  • Spectral flow
  • Three manifolds

ASJC Scopus subject areas

  • Mathematics(all)

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