Equivariant Localization of $K$-homological Euler Class for almost connected Lie Groups
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909746321162240 |
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| author | Liu, Hongzhi Wang, Hang Wang, Zijing Xiang, Shaocong |
| author_facet | Liu, Hongzhi Wang, Hang Wang, Zijing Xiang, Shaocong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21415 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant Localization of $K$-homological Euler Class for almost connected Lie Groups Liu, Hongzhi Wang, Hang Wang, Zijing Xiang, Shaocong Operator Algebras Functional Analysis K-Theory and Homology 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. |
| title | Equivariant Localization of $K$-homological Euler Class for almost connected Lie Groups |
| topic | Operator Algebras Functional Analysis K-Theory and Homology |
| url | https://arxiv.org/abs/2507.21415 |