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Stackings and the W-cycles Conjecture

Published online by Cambridge University Press:  20 November 2018

Larsen Louder  and
Henry Wilton
Larsen Louder
Affiliation:
University College London, London, UK. e-mail: l.louder@ucl.ac.uk
Henry Wilton
Affiliation:
University of Cambridge, Cambridge, UK. e-mail: h.wilton@maths.cam.ac.uk
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Abstract

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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.

Keywords

20F65free groupsone-relator groupsright-orderability

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 3 , 01 September 2017 , pp. 604 - 612
Copyright
Copyright © Canadian Mathematical Society 2017

References

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