The verbal width of acylindrically hyperbolic groups

Bestvina, Mladen; Bromberg, Kenneth; Fujiwara, Koji

doi:10.2140/agt.2019.19.477

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The verbal width of acylindrically hyperbolic groups

Mladen Bestvina, Kenneth Bromberg and Koji Fujiwara

Algebraic & Geometric Topology 19 (2019) 477–489

DOI: 10.2140/agt.2019.19.477

Abstract

We show that the verbal width is infinite for acylindrically hyperbolic groups, which include hyperbolic groups, mapping class groups and $Out (F_{n})$ .

Keywords

verbal subgroups, acylindrically hyperbolic groups, quasimorphisms

Mathematical Subject Classification 2010

Primary: 20F65, 20F67

References

Publication

Received: 11 April 2018

Revised: 30 June 2018

Accepted: 20 August 2018

Published: 6 February 2019

Authors

Mladen Bestvina
Department of Mathematics University of Utah Salt Lake City, UT United States

Kenneth Bromberg
Department of Mathematics University of Utah Salt Lake City, UT United States

Koji Fujiwara
Department of Mathematics Kyoto University Kyoto Japan

Volume 19, issue 1 (2019)