Computing the twisted $L^2$-Euler characteristic
Geometric Topology
2025-03-11 v3
Abstract
We present an algorithm that computes Friedl and L\"uck's twisted -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.
Cite
@article{arxiv.2310.07024,
title = {Computing the twisted $L^2$-Euler characteristic},
author = {Jacopo G. Chen},
journal= {arXiv preprint arXiv:2310.07024},
year = {2025}
}
Comments
48 pages, 5 figures. Replaced to match the journal version. An implementation of the algorithm can be found on GitHub at https://github.com/floatingpoint-754/twisted-l2-characteristic