Computing the twisted $L^2$-Euler characteristic
| Autor: | Chen, Jacopo G. |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We present an algorithm that computes Friedl and L\"uck's twisted $L^2$-Euler characteristic for a suitable regular CW complex, employing Oki's matrix expansion algorithm to indirectly evaluate the Dieudonn\'e 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. Comment: 55 pages, 5 figures. Fixed typos, added acknowledgments, added Remark 6.7 |
| Databáze: | arXiv |
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