Common finite covers and quasitreesMPIM

by Martin Bridson (University of Oxford)

Thursday Jan 29, 2026, 4:30 PM → 6:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Oberseminar Differentialgeometrie

Sam Shepherd and I proved that if two finite simplicial complexes have isomorphic universal covers and free fundamental groups, then they have a common finite cover. In the 1-dimensional case (graphs), this is Leighton's Theorem. I shall discuss various extensions of Leighton's Theorem and examples that illustrate its limitations, with a focus on coverings by quasitrees. I shall then outline a proof of our theorem, which involves the construction of auxiliary CAT(0) cube complexes.