Operator Algebras Seminar: A Localization-Algebra Approach to the Equivariant Poincaré–Hopf Theorem

Speaker: 向少聪 (华东师范大学)

Time: 2026-03-05 13:00-14:00
Location: 1402, SIMIS

摘要：

In this talk, we sketch how localization algebras can be used to represent the equivariant $K$-homology class of the Euler characteristic operator $d+d^*$ on a cocompact proper $\Gamma$-manifold, where $\Gamma$ is a discrete group. Motivated by Witten deformation, we indicate how this class can be localized—within equivariant $K$-homology—to neighborhoods of the zero set of a $\Gamma$-equivariant Morse-type vector field. As an application, we recover the classical Poincaré–Hopf formula and obtain its equivariant generalization.