Year: 2026
Type: article
Abstract: For all $$k \ge 2$$ k ≥ 2 , we show that there exists a group G and a non-free stably free $$\mathbb {Z}G$$ Z G -module of rank k . We use this to show that, for all $$k \ge 2$$ k ≥ 2 , there exist homotopically distinct finite 2-complexes with fundamental group G and with Euler characteristic exceeding the minimal value over G by k . This resolves Problem D5 in the 1979 Problem List of C. T. C. Wall. We also explore a number of generalisations and present a potential application to the topology of closed smooth 4-manifolds.
Source: Mathematische Annalen
Author: John Nicholson
Institution: University of Glasgow
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7130429587