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

2023/01/09 by Hans Bodén, Boden, Hans U, Christopher M. Herald +3 · 1 citation
Mathematics · #57K18 #57K31 #57R58 #81T13 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2301.03676

openalex publication_date 2023/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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