Hyperbolic immersions of free groups

Jean Pierre Mutanguha

doi:10.4171/GGD/580

Hyperbolic immersions of free groups

Jean Pierre Mutanguha

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We prove that the mapping torus of a graph immersion has a word-hyperbolic fundamental group if and only if the corresponding endomorphism does not produce Baumslag–Solitar subgroups. Due to a result by Reynolds, this theorem applies to all injective endomorphisms of F₂ and nonsurjective fully irreducible endomorphisms of F_n.

Original language	English (US)
Pages (from-to)	1253-1275
Number of pages	23
Journal	Groups, Geometry, and Dynamics
Volume	14
Issue number	4
DOIs	https://doi.org/10.4171/GGD/580
State	Published - 2021
Externally published	Yes

All Science Journal Classification (ASJC) codes

Geometry and Topology
Discrete Mathematics and Combinatorics

Keywords

Combination theorem
Graph immersions
Nonsurjective endomorphisms
Word-hyperbolic

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10.4171/GGD/580

Cite this

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title = "Hyperbolic immersions of free groups",

abstract = "We prove that the mapping torus of a graph immersion has a word-hyperbolic fundamental group if and only if the corresponding endomorphism does not produce Baumslag–Solitar subgroups. Due to a result by Reynolds, this theorem applies to all injective endomorphisms of F2 and nonsurjective fully irreducible endomorphisms of Fn.",

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note = "Publisher Copyright: {\textcopyright} European Mathematical Society",

year = "2021",

doi = "10.4171/GGD/580",

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AU - Mutanguha, Jean Pierre

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AB - We prove that the mapping torus of a graph immersion has a word-hyperbolic fundamental group if and only if the corresponding endomorphism does not produce Baumslag–Solitar subgroups. Due to a result by Reynolds, this theorem applies to all injective endomorphisms of F2 and nonsurjective fully irreducible endomorphisms of Fn.

KW - Combination theorem

KW - Graph immersions

KW - Nonsurjective endomorphisms

KW - Word-hyperbolic

UR - https://www.scopus.com/pages/publications/85099042523

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DO - 10.4171/GGD/580

M3 - Article

AN - SCOPUS:85099042523

SN - 1661-7207

VL - 14

SP - 1253

EP - 1275

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 4

ER -

Hyperbolic immersions of free groups

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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