Examples of homology 3-spheres whose Chern-Simons function is not Morse-Bott

Abstract

We construct two homology 3-spheres for which the (unperturbed) $SU(2)$ Chern-Simons function is not Morse-Bott. In one case, there is a degenerate isolated critical point. In the other, a path component of the critical set is not homeomorphic to a manifold. The examples are $+1$ surgeries on connected sums of torus knots.

8 pages, 5 figures