Year: 2026
Type: preprint
Abstract: A negative answer to Whitehead's asphericity problem would follow from an infinite chain of two-complexes, starting with a non-aspherical one, in which every inclusion induces the zero map on second homotopy groups. We prove that a connected two-complex $K$ is the first term of such chains of every \emph{finite} length if and only if $K$ has a connected acyclic regular cover. In particular, there is a finite non-aspherical two-complex $K$, a presentation complex of $\mathrm{SL}(2,5)$, such that for every $n$ there is a strictly increasing chain of finite two-complexes $K=K_0\subset K_1\subset\dots\subset K_n$ in which all inclusions are zero on $π_2$.
Source: arXiv (Cornell University)
Authors: Bartholdi, Laurent, Mikhailov, Roman
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220923162