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Computing the twisted $L^2$-Euler characteristic

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arxiv 2310.07024 v3 pith:H7EPTLZD submitted 2023-10-10 math.GT

Jacopo G. Chen This is my paper · ORCID
classification math.GT
keywords algorithmcharacteristiceulertwistedcasescensuscertifyclosed
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Thurston norm of graph manifolds

    math.GT 2024-12 conditional novelty 7.0 of 10

    Norms that are sums of absolute values of rational linear functionals are exactly the nonvanishing Thurston norms of closed oriented graph manifolds, which can be chosen to fiber over the circle or not.

  2. RL-Driven Data Generation for Robust Vision-Based Dexterous Grasping

    cs.RO 2025-04 conditional novelty 6.0 of 10

    A vision-based dexterous grasping policy trained on RL-generated simulated trajectories mixed with 40 real demonstrations achieves 100% real-world success on all tested objects.

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