Stackings and the W-cycles Conjecture. Issue 3 (1st September 2017) - Louder, Larsen; Wilton, Henry
Abstract: We prove Wise's W -cycles conjecture. Consider a compact graph Γ ' immersing into another graph Γ . For any immersed cycle Λ :S^1→ Γ , we consider the map Λ ' from the circular components S of the pullback to Γ ' . Unless Λ ' is reducible, the degree of the covering map S→ S^1 is bounded above by minus the Euler characteristic of Γ ' . As a corollary, any finitely generated subgroup of a one-relator group has a finitely generated Schur multiplier.