Equivariant Cerf theory and perturbative SU(n) Casson invariants
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 3, and write down an explicit formula when n D 4. This generalizes the previous works of Boden and Herald (1998) and Herald (2006).
Fields of Study & Subjects
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Geometry & Topology
- Publisher
- Mathematical Sciences Publishers
- Volume
- 30
- Issue
- 4
- Pages
- 1203–1276
- Publication date
- 9 July 2026
- Language
- EN