Folding-like techniques for CAT(0) cube complexes. (28th July 2022)

• Record Type: Journal Article
• Authors: BEN–ZVI, MICHAEL; KROPHOLLER, ROBERT; LYMAN, RYLEE ALANZA
• Is Part Of: Mathematical proceedings of the Cambridge Philosophical Society. Volume 173:Part 1(2022)
• Page Start: 227
• Page End: 238
• Publication Date: 2022-07-28
• Subjects: 20F65 -- 20F67; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S0305004121000645
• Languages: English
• ISSNs: 0305-0041

Abstract

Abstract: In a seminal paper, Stallings introduced folding of morphisms of graphs. One consequence of folding is the representation of finitely-generated subgroups of a finite-rank free group as immersions of finite graphs. Stallings's methods allow one to construct this representation algorithmically, giving effective, algorithmic answers and proofs to classical questions about subgroups of free groups. Recently Dani–Levcovitz used Stallings-like methods to study subgroups of right-angled Coxeter groups, which act geometrically on CAT(0) cube complexes. In this paper we extend their techniques to fundamental groups of non-positively curved cube complexes.