2020/09/02 by Bai, Shaoyun, Zhang, Boyu
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2009.01118
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=4. This generalizes the previous works of Boden and Herald.