Stackings and the W-cycles conjecture
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Louder, L
Wilton, Henry https://orcid.org/0000-0001-6369-9478
Abstract
We prove Wise’s W-cycles conjecture: Consider a compact graph Γ′ immersing into another graph Γ. For any immersed cycle Λ : S¹ → 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 → S¹ is bounded above by minus the Euler characteristic of Γ′. As a corollary, any finitely generated subgroup of a one-relator group has finitely generated Schur multiplier.
Description
Keywords
free groups, one-relator groups, right-orderability
Journal Title
Canadian Mathematical Bulletin
Conference Name
Journal ISSN
0008-4395
1496-4287
1496-4287
Volume Title
Publisher
Canadian Mathematical Society
Publisher DOI
Sponsorship
EPSRC