- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:58
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
2
2008
1
Rips construction and Kazhdan property (T)
Igor
Belegradek
Georgia Institute of Technology, ATLANTA, UNITED STATES
Denis
Osin
Vanderbilt University, NASHVILLE, UNITED STATES
Hyperbolic group, Rips construction, Kazhdan property (T)
We show that for any non-elementary hyperbolic group H and any finitely presented group Q, there exists a short exact sequence 1 → N → G → Q → 1, where G is a hyperbolic group and N is a quotient group of H. As an application we construct a hyperbolic group that has the same n-dimensional complex representations as a given finitely generated group, show that adding relations of the form xn = 1 to a presentation of a hyperbolic group may drastically change the group even in case n ≫ 1, and prove that some properties (e.g. properties (T) and FA) are not recursively recognizable in the class of hyperbolic groups. A relatively hyperbolic version of this theorem is also used to generalize results of Ollivier–Wise on outer automorphism groups of Kazhdan groups.
Group theory and generalizations
General
1
12
10.4171/GGD/29
http://www.ems-ph.org/doi/10.4171/GGD/29