Stackings and the W-cycles Conjecture. Issue 3 (1st September 2017)

• Record Type: Journal Article
• Authors: Louder, Larsen; Wilton, Henry
• Is Part Of: Canadian mathematical bulletin =. Volume 60:Issue 3(2017)
• Page Start: 604
• Page End: 612
• Publication Date: 2017-09-01
• Subjects: 20F65; free groups -- one-relator groups -- right-orderability; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2016-078-3
• Languages: English
• ISSNs: 0008-4395

Abstract

Abstract: We prove Wise's $W$ -cycles conjecture. Consider a compact graph $\Gamma '$ immersing into another graph $\Gamma $ . For any immersed cycle $\Lambda :{{S}^{1}}\to \Gamma $, we consider the map $\Lambda '$ from the circular components $\mathbb{S}$ of the pullback to $\Gamma '$ . Unless $\Lambda '$ is reducible, the degree of the covering map $\mathbb{S}\to {{S}^{1}}$ is bounded above by minus the Euler characteristic of $\Gamma '$ . As a corollary, any finitely generated subgroup of a one-relator group has a finitely generated Schur multiplier.