Cubulating hyperbolic free-by-cyclic groups: The irreducible case

Mark F. Hagen; Daniel T. Wise

doi:10.1215/00127094-3450752

Cubulating hyperbolic free-by-cyclic groups: The irreducible case

Mark F. Hagen, Daniel T. Wise

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

22 Citations (Scopus)

312 Downloads (Pure)

Abstract

Let V be a finite graph, and let ϕ:V→V be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group G. Then G acts freely and cocompactly on a CAT(0) cube complex. Hence, if F is a finite-rank free group and if Φ:F→F is an irreducible monomorphism so that G=F∗Φ is word-hyperbolic, then G acts freely and cocompactly on a CAT(0) cube complex. This holds, in particular, if Φ is an irreducible automorphism with G=F⋊ΦZ word-hyperbolic.

Original language	English
Pages (from-to)	1753-1813
Number of pages	61
Journal	Duke Mathematical Journal
Volume	165
Issue number	9
Early online date	24 Mar 2016
DOIs	https://doi.org/10.1215/00127094-3450752
Publication status	Published - 15 Jun 2016

Keywords

math.GR

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10.1215/00127094-3450752

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Dr Mark F Hagen
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title = "Cubulating hyperbolic free-by-cyclic groups: The irreducible case",

abstract = "Let V be a finite graph, and let ϕ:V→V be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group G. Then G acts freely and cocompactly on a CAT(0) cube complex. Hence, if F is a finite-rank free group and if Φ:F→F is an irreducible monomorphism so that G=F∗Φ is word-hyperbolic, then G acts freely and cocompactly on a CAT(0) cube complex. This holds, in particular, if Φ is an irreducible automorphism with G=F⋊ΦZ word-hyperbolic.",

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AU - Wise, Daniel T.

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N2 - Let V be a finite graph, and let ϕ:V→V be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group G. Then G acts freely and cocompactly on a CAT(0) cube complex. Hence, if F is a finite-rank free group and if Φ:F→F is an irreducible monomorphism so that G=F∗Φ is word-hyperbolic, then G acts freely and cocompactly on a CAT(0) cube complex. This holds, in particular, if Φ is an irreducible automorphism with G=F⋊ΦZ word-hyperbolic.

AB - Let V be a finite graph, and let ϕ:V→V be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group G. Then G acts freely and cocompactly on a CAT(0) cube complex. Hence, if F is a finite-rank free group and if Φ:F→F is an irreducible monomorphism so that G=F∗Φ is word-hyperbolic, then G acts freely and cocompactly on a CAT(0) cube complex. This holds, in particular, if Φ is an irreducible automorphism with G=F⋊ΦZ word-hyperbolic.

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M3 - Article (Academic Journal)

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SP - 1753

EP - 1813

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 9

ER -

Cubulating hyperbolic free-by-cyclic groups: The irreducible case

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