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Stackings and the W-cycles Conjecture
Published online by Cambridge University Press: 20 November 2018
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.
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- Copyright © Canadian Mathematical Society 2017
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