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COHERENCE, LOCAL INDICABILITY AND NONPOSITIVE IMMERSIONS
Published online by Cambridge University Press: 17 September 2020
Abstract
We examine 2-complexes $X$ with the property that for any compact connected
$Y$, and immersion
$Y\rightarrow X$, either
$\unicode[STIX]{x1D712}(Y)\leqslant 0$ or
$\unicode[STIX]{x1D70B}_{1}Y=1$. The mapping torus of an endomorphism of a free group has this property. Every irreducible 3-manifold with boundary has a spine with this property. We show that the fundamental group of any 2-complex with this property is locally indicable. We outline evidence supporting the conjecture that this property implies coherence. We connect the property to asphericity. Finally, we prove coherence for 2-complexes with a stricter form of this property. As a corollary, every one-relator group with torsion is coherent.
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 2 , March 2022 , pp. 659 - 674
- Copyright
- © The Author(s) 2020. Published by Cambridge University Press
Footnotes
Research supported by NSERC.
References
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