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arXiv · 2009.01118

Equivariant Cerf theory and perturbative $SU(n)$ Casson invariants

Shaoyun Bai·Boyu Zhang
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Abstract

We develop an equivariant Cerf theory for Morse functions on finite-dimensional manifolds with group actions, and adapt the technique to the infinite-dimensional setting to study the moduli space of perturbed flat $SU(n)$-connections. As a consequence, we prove the existence of perturbative $SU(n)$ Casson invariants on integer homology spheres for all $n\ge 3$, and write down an explicit formula when $n=4$. This generalizes the previous works of Boden and Herald.

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Shaoyun Bai, Boyu Zhang. 2020-09-02. Equivariant Cerf theory and perturbative $SU(n)$ Casson invariants. https://doi.org/10.2140/gt.2026.30.1203

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