On the Uniqueness of the $G$-Equivariant Spectral Flow
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914422011723776 |
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| author | Izydorek, Marek Janczewska, Joanna Starostka, Maciej Waterstraat, Nils |
| author_facet | Izydorek, Marek Janczewska, Joanna Starostka, Maciej Waterstraat, Nils |
| contents | The spectral flow is an integer-valued homotopy invariant for paths of selfadjoint Fredholm operators. Lesch as well as Pejsachowicz, Fitzpatrick and Ciriza independently showed that it is uniquely characterised by its elementary properties. The authors recently introduced a $G$-equivariant spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the action of a compact Lie group $G$. The purpose of this paper is to show that the $G$-equivariant spectral flow is uniquely characterised by the same elementary properties when appropriately restated. As an application, we introduce an alternative definition of the $G$-equivariant spectral flow via a $G$-equivariant Maslov index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Uniqueness of the $G$-Equivariant Spectral Flow Izydorek, Marek Janczewska, Joanna Starostka, Maciej Waterstraat, Nils Functional Analysis Spectral Theory The spectral flow is an integer-valued homotopy invariant for paths of selfadjoint Fredholm operators. Lesch as well as Pejsachowicz, Fitzpatrick and Ciriza independently showed that it is uniquely characterised by its elementary properties. The authors recently introduced a $G$-equivariant spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the action of a compact Lie group $G$. The purpose of this paper is to show that the $G$-equivariant spectral flow is uniquely characterised by the same elementary properties when appropriately restated. As an application, we introduce an alternative definition of the $G$-equivariant spectral flow via a $G$-equivariant Maslov index. |
| title | On the Uniqueness of the $G$-Equivariant Spectral Flow |
| topic | Functional Analysis Spectral Theory |
| url | https://arxiv.org/abs/2508.01061 |