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Quantum SO(3)-invariants dominate the SU(2)-invariant of Casson and Walker

Published online by Cambridge University Press:  24 October 2008

Hitoshi Murakami
Hitoshi Murakami
Affiliation:
Department of Mathematics, Osaka City university, Sugimoto, Sumiyoshi-ku, Osaka 558, Japan, E-mail address: h1653@ocugw.cc.osaka-cu.ac.jp
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For a compact Lie group G, E. Witten proposed topological invariants of a threemanifold (quantum G-invariants) in 1988 by using the Chern-Simons functional and the Feynman path integral [30]. See also [2]. N. Yu. Reshetikhin and V. G. Turaev gave a mathematical proof of existence of such invariants for G = SU(2) [28]. R. Kirby and P. Melvin found that the quantum SU(2)-invariant associated to q = exp(2π √ − 1/r) with r odd splits into the product of the quantum SO(3)-invariant and [15]. For other approaches to these invariants, see [3, 4, 5, 16, 22, 27].

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 2 , March 1995 , pp. 237 - 249
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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