The Euler Class and Flux Homomorphisms under Non-Orientability
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913996254216192 |
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| author | Kim, KyeongRo Maruyama, Shuhei |
| author_facet | Kim, KyeongRo Maruyama, Shuhei |
| contents | For an orientable surface with an area form, there are two invariants of area-preserving dynamics, the flux homomorphism and the Calabi invariant. Tsuboi found a remarkable connection between the Calabi invariant on the closed disk and a topological invariant -- the Euler class. In this paper, we investigate a relationship between the Euler class and the flux homomorphism for non-orientable compact surfaces with one boundary component. Furthermore, we prove the simplicity of the kernel of the flux homomorphisms in this non-orientable setting, which implies the non-existence of invariants analogous to the Calabi invariant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_12874 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Euler Class and Flux Homomorphisms under Non-Orientability Kim, KyeongRo Maruyama, Shuhei Geometric Topology For an orientable surface with an area form, there are two invariants of area-preserving dynamics, the flux homomorphism and the Calabi invariant. Tsuboi found a remarkable connection between the Calabi invariant on the closed disk and a topological invariant -- the Euler class. In this paper, we investigate a relationship between the Euler class and the flux homomorphism for non-orientable compact surfaces with one boundary component. Furthermore, we prove the simplicity of the kernel of the flux homomorphisms in this non-orientable setting, which implies the non-existence of invariants analogous to the Calabi invariant. |
| title | The Euler Class and Flux Homomorphisms under Non-Orientability |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2508.12874 |