A perturbative SU (3) Casson invariant

Autor: Edward Y. Miller, Ronnie Lee, Sylvain E. Cappell
Rok vydání: 2002
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Zdroj: Commentarii Mathematici Helvetici. 77:491-523
ISSN: 1420-8946
0010-2571
DOI: 10.1007/s00014-002-8349-8
Popis: A perturbative SU(3) Casson invariant \( \Lambda_{SU(3)}(X) \) for integral homology 3-sphere is defined. Besides being fully perturbative, it has the nice properties: (1) \( 4\cdot \Lambda_{SU(3)} \) 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.
Databáze: OpenAIRE
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