Computing the twisted $L^2$-Euler characteristic
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913725894623232 |
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| author | Chen, Jacopo G. |
| author_facet | Chen, Jacopo G. |
| contents | We present an algorithm that computes Friedl and Lück's twisted $L^2$-Euler characteristic for a suitable regular CW complex, employing Oki's matrix expansion algorithm to indirectly evaluate the Dieudonné determinant. The algorithm needs to run for an extremely long time to certify its outputs, but a truncated, human-assisted version produces very good results in many cases, such as hyperbolic link complements, closed census 3-manifolds, free-by-cyclic groups, and higher-dimensional examples, such as the fiber of the Ratcliffe-Tschantz manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07024 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Computing the twisted $L^2$-Euler characteristic Chen, Jacopo G. Geometric Topology 57-08 (Primary) 12E15, 20C07, 57K32, 57K50 (Secondary) We present an algorithm that computes Friedl and Lück's twisted $L^2$-Euler characteristic for a suitable regular CW complex, employing Oki's matrix expansion algorithm to indirectly evaluate the Dieudonné determinant. The algorithm needs to run for an extremely long time to certify its outputs, but a truncated, human-assisted version produces very good results in many cases, such as hyperbolic link complements, closed census 3-manifolds, free-by-cyclic groups, and higher-dimensional examples, such as the fiber of the Ratcliffe-Tschantz manifold. |
| title | Computing the twisted $L^2$-Euler characteristic |
| topic | Geometric Topology 57-08 (Primary) 12E15, 20C07, 57K32, 57K50 (Secondary) |
| url | https://arxiv.org/abs/2310.07024 |