Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

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

Hitoshi Murakamia1*

a1 Department of Mathematics, Osaka City university, Sugimoto, Sumiyoshi-ku, Osaka 558, Japan, E-mail address:

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 S0305004100073084_inline1 associated to q = exp(2π √ − 1/r) with r odd splits into the product of the quantum SO(3)-invariant S0305004100073084_inline2 and S0305004100073084_inline3 [15]. For other approaches to these invariants, see [3, 4, 5, 16, 22, 27].

(Received January 31 1994)


* Partially supported by Grant-in-Aid for Scientific Research on Priority Areas 231 ‘Infinite Analysis’.