Work

Equivariant Localization of $K$-homological Euler Class for almost connected Lie Groups

Year: 2025

Type: preprint

Abstract: Using the Witten deformation and localization algebra techniques, we compute the $G$-equivariant $K$-homology class of the de Rham operator on a proper cocompact $G$-spin manifold, where $G$ is an almost connected Lie group. By applying a $G$-invariant Morse-Bott perturbation, this class is localized near the zero set of the perturbation and can be identified explicitly with an element in the representation rings associated to some isotropy subgroups. The result yields an equivariant Poincaré-Hopf formula and supplies concise tools for equivariant index computations.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2507.21415

Authors: Liu, Hongzhi, Wang, Hang, Wang, Zijing, Xiang, Shaocong

Institutions: Shanghai University of Finance and Economics, East China Normal University, Fudan University

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Science and Technology Commission of Shanghai Municipality

Awards: G1037693139, G1609915050, G2408283191, G3745923048, G6806139685, G7270659173, 高指标理论中的不变量

OpenAlex ID: W6929353897

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