A perturbative SU(3) Casson invariant

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

doi:10.1007/s00014-002-8349-8

A perturbative SU(3) Casson invariant

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

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A perturbative SU(3) Casson invariant ΛA_SU (X) for integral homology 3-sphere is defined. Besides being fully perturbative, it has the nice properties: (1) 4 · Λ_SU(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 language	English (US)
Pages (from-to)	491-523
Number of pages	33
Journal	Commentarii Mathematici Helvetici
Volume	77
Issue number	3
DOIs	https://doi.org/10.1007/s00014-002-8349-8
State	Published - 2002

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.1007/s00014-002-8349-8

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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.",

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AU - Cappell, S. E.

AU - Lee, R.

AU - Miller, E. Y.

PY - 2002

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AB - 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.

KW - Chern-Simons

KW - Eta invariant

KW - Floer homology

KW - Gauge theory

KW - Heegard decomposition

KW - Index theory

KW - Malsov index

KW - Spectral flow

KW - Three manifolds

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A perturbative SU(3) Casson invariant

Abstract

Keywords

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