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

Abstract

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 ].