Quantum<i>SU</i>(2)-invariants dominate Casson's<i>SU</i>(2)-invariant

Abstract

In 1988, E. Witten proposed an array of invariants (quantum G -invariants) for a 3-manifold associated with a compact simple Lie group G based on the quantum field theory [ 22 ]. N. Reshetikhin and V. Turaev [ 20 ] gave a mathematical approach to these invariants for G = SU (2) by using representations of the quantum group U q ( sl (2, ℂ)). See also [ 2, 11, 12, 14, 15, 16 ] for other approaches to these invariants: [ 16 ] may be the simplest way (for knot theorists) to understand the existence of these invariants.