Seminar| Institute of Mathematical Sciences
Time: Friday, January 30th, 2026,09:30-11:00
Location: IMS, RS408
Speaker: Jacopo Chen, Shanghai Institute for Mathematics and Interdisciplinary Sciences(SIMIS)
Abstract: The twisted $L^2$-Euler characteristic is an invariant for CW complexes introduced by Friedl and Lück, generalizing the Thurston norm. We present an algorithm for the computation of this invariant, employing Oki’s matrix expansion algorithm to indirectly evaluate the Dieudonné determinant of certain matrices obtained from the cellular chain complex. 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 5-manifold. Inspired by the results of these experiments, we proceed to state a few conjectures and related heuristics about the twisted $L^2$-Euler characteristic.