Comments on Witten Invariants of 3-Manifolds for SU(2) and $Z_m$

Abstract

The values of the Witten invariants, $I_W$, of the lens space $L(p,1)$ for SU(2) at level $k$ are obtained for arbitrary $p$. A duality relation for $I_W$ when $p$ and $k$ are interchanged, valid for asymptotic $k$, is observed. A method for calculating $I_W$ for any group $G$ is described. It is found that $I_W$ for $Z_m$, even for $m=2$, distinguishes 3-manifolds quite effectively.

14 pages ; 6 figures not included, available in hard copy upon request. TCD-2-93