McMullen polynomials and Lipschitz flows for free-by-cyclic groups

Spencer Dowdall; Ilya Kapovich; Christopher J. Leininger

doi:10.4171/JEMS/739

McMullen polynomials and Lipschitz flows for free-by-cyclic groups

Spencer Dowdall, Ilya Kapovich, Christopher J. Leininger

Mathematics

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

Abstract

Consider a group G and an epimorphism u0 V G→ Z inducing a splitting of G as a semidirect product ker(u0)Z with ker(u0) a finitely generated free group and ϵOut ker (u 0)representable by an expanding irreducible train track map. Building on our earlier work [DKL], in which we realized G as π1(X) for an Eilenberg-MacLane 2-complex X equipped with a semiflow , and inspired by McMullen's Teichmüller polynomial for fibered hyperbolic 3-manifolds, we construct a polynomial invariant mϵ ZTH₁(G;Z)=torsionU for (X,) and investigate its properties [EQUATION PRESENTED].

Original language	English (US)
Pages (from-to)	3253-3353
Number of pages	101
Journal	Journal of the European Mathematical Society
Volume	19
Issue number	11
DOIs	https://doi.org/10.4171/JEMS/739
State	Published - 2017

Keywords

BNS-Invariant
Free-By-Cyclic groups
Stretch Factors
Train Track Maps

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Online availability

10.4171/JEMS/739

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title = "McMullen polynomials and Lipschitz flows for free-by-cyclic groups",

abstract = "Consider a group G and an epimorphism u0 V G→ Z inducing a splitting of G as a semidirect product ker(u0)Z with ker(u0) a finitely generated free group and ϵOut ker (u 0)representable by an expanding irreducible train track map. Building on our earlier work [DKL], in which we realized G as π1(X) for an Eilenberg-MacLane 2-complex X equipped with a semiflow , and inspired by McMullen's Teichm{\"u}ller polynomial for fibered hyperbolic 3-manifolds, we construct a polynomial invariant mϵ ZTH1(G;Z)=torsionU for (X,) and investigate its properties [EQUATION PRESENTED].",

keywords = "BNS-Invariant, Free-By-Cyclic groups, Stretch Factors, Train Track Maps",

author = "Spencer Dowdall and Ilya Kapovich and Leininger, {Christopher J.}",

note = "Funding Information: The first author was partially supported by the NSF postdoctoral fellowship, NSF MSPRF no. 1204814. The second author was partially supported by the NSF grant DMS-0904200, DMS-1405146 and by the Simons Foundation Collaboration grant no. 279836. The third author was partially supported by the NSF grant DMS-1207183 and acknowledges support from NSF grants DMS 1107452, 1107263, 1107367 (the “GEAR Network”). Publisher Copyright: {\textcopyright} 2017 European Mathematical Society.",

year = "2017",

doi = "10.4171/JEMS/739",

language = "English (US)",

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T1 - McMullen polynomials and Lipschitz flows for free-by-cyclic groups

AU - Dowdall, Spencer

AU - Kapovich, Ilya

AU - Leininger, Christopher J.

N1 - Funding Information: The first author was partially supported by the NSF postdoctoral fellowship, NSF MSPRF no. 1204814. The second author was partially supported by the NSF grant DMS-0904200, DMS-1405146 and by the Simons Foundation Collaboration grant no. 279836. The third author was partially supported by the NSF grant DMS-1207183 and acknowledges support from NSF grants DMS 1107452, 1107263, 1107367 (the “GEAR Network”). Publisher Copyright: © 2017 European Mathematical Society.

PY - 2017

Y1 - 2017

N2 - Consider a group G and an epimorphism u0 V G→ Z inducing a splitting of G as a semidirect product ker(u0)Z with ker(u0) a finitely generated free group and ϵOut ker (u 0)representable by an expanding irreducible train track map. Building on our earlier work [DKL], in which we realized G as π1(X) for an Eilenberg-MacLane 2-complex X equipped with a semiflow , and inspired by McMullen's Teichmüller polynomial for fibered hyperbolic 3-manifolds, we construct a polynomial invariant mϵ ZTH1(G;Z)=torsionU for (X,) and investigate its properties [EQUATION PRESENTED].

AB - Consider a group G and an epimorphism u0 V G→ Z inducing a splitting of G as a semidirect product ker(u0)Z with ker(u0) a finitely generated free group and ϵOut ker (u 0)representable by an expanding irreducible train track map. Building on our earlier work [DKL], in which we realized G as π1(X) for an Eilenberg-MacLane 2-complex X equipped with a semiflow , and inspired by McMullen's Teichmüller polynomial for fibered hyperbolic 3-manifolds, we construct a polynomial invariant mϵ ZTH1(G;Z)=torsionU for (X,) and investigate its properties [EQUATION PRESENTED].

KW - BNS-Invariant

KW - Free-By-Cyclic groups

KW - Stretch Factors

KW - Train Track Maps

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McMullen polynomials and Lipschitz flows for free-by-cyclic groups

Abstract

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