QuantumSU(2)-invariants dominate Casson'sSU(2)-invariant

Abstract

In 1988, E. Witten proposed an array of invariants (quantumG-invariants) for a 3-manifold associated with a compact simple Lie groupGbased on the quantum field theory [22]. N. Reshetikhin and V. Turaev [20] gave a mathematical approach to these invariants forG=SU(2) by using representations of the quantum groupUq(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.