Open Research Index

Finite Chains of Two-Complexes and Acyclic Covers

Laurent Bartholdi, Roman Mikhailov

Palomar Registrypalomar/PALOMAR-2026-10-09-000008Oct 9, 2026math.GTscore 0

Whitehead's asphericity problem would have a negative answer if a non-aspherical two-complex began an infinite chain whose inclusions induce zero maps on second homotopy groups. This Lean formalization proves the article's main finite-length characterization: a connected two-complex K begins such chains of every finite length if and only if K has a connected acyclic regular cover. It also formalizes the finite acyclic enhancement.

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