The geometry of purely loxodromic subgroups of right-angled Artin groups
Authors:
Thomas Koberda, Johanna Mangahas and Samuel J. Taylor
Journal:
Trans. Amer. Math. Soc. 369 (2017), 8179-8208
MSC (2010):
Primary 20F36; Secondary 57M07
DOI:
https://doi.org/10.1090/tran/6933
Published electronically:
June 13, 2017
MathSciNet review:
3695858
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups
. In particular, such subgroups are quasiconvex in
. In addition, we identify a milder condition for a finitely generated subgroup of
that guarantees it is free, undistorted, and retains finite generation when intersected with
for subgraphs
of
. These results have applications to both the study of convex cocompactness in
and the way in which certain groups can embed in right-angled Artin groups.
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Additional Information
Thomas Koberda
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904-4137
Email:
thomas.koberda@gmail.com
Johanna Mangahas
Affiliation:
Department of Mathematics, 244 Mathematics Building, University at Buffalo, Buffalo, New York 14260
Email:
mangahas@buffalo.edu
Samuel J. Taylor
Affiliation:
Department of Mathematics, 10 Hillhouse Ave, Yale University, New Haven, Connecticut 06520
Address at time of publication:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email:
samuel.taylor@temple.edu
DOI:
https://doi.org/10.1090/tran/6933
Keywords:
Right-angled Artin group,
extension graph,
convex cocompact subgroup,
loxodromic isometry
Received by editor(s):
January 5, 2015
Received by editor(s) in revised form:
January 27, 2016, and March 8, 2016
Published electronically:
June 13, 2017
Article copyright:
© Copyright 2017
American Mathematical Society