scholarly journals Comparing the Roller and B(X) boundaries of Cat(0) cube complexes

2021 ◽  
Author(s):  
Ivan Levcovitz
Keyword(s):  
Cube Complexes

scholarly journals Property A and CAT(0) cube complexes

2009 ◽  
Vol 256 (5) ◽  
pp. 1408-1431 ◽  
Author(s):  
J. Brodzki ◽  
S.J. Campbell ◽  
E. Guentner ◽  
G.A. Niblo ◽  
N.J. Wright
Keyword(s):  
Property A ◽  
Cube Complexes

scholarly journals Ping Pong on CAT(0) cube complexes

2016 ◽  
Vol 91 (3) ◽  
pp. 543-561 ◽  
Author(s):  
Aditi Kar ◽  
Michah Sageev
Keyword(s):  
Ping Pong ◽  
Cube Complexes

scholarly journals Hyperplanes of Squier’s cube complexes

2018 ◽  
Vol 18 (6) ◽  
pp. 3205-3256 ◽  
Author(s):  
Anthony Genevois
Keyword(s):  
Cube Complexes

scholarly journals Hyperbolicities in CAT(0) cube complexes

2020 ◽  
Vol 65 (1) ◽  
pp. 33-100
Author(s):  
Anthony Genevois
Keyword(s):  
Cube Complexes

scholarly journals On groups whose actions on finite-dimensional CAT(0) spaces have global fixed points

2019 ◽  
Vol 22 (6) ◽  
pp. 1089-1099
Author(s):  
Motoko Kato
Keyword(s):  
Fixed Points ◽  
Topological Dimension ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Thompson’S Group ◽  
Simple Action ◽  
Cube Complexes

Abstract We give a criterion for group elements to have fixed points with respect to a semi-simple action on a complete CAT(0) space of finite topological dimension. As an application, we show that Thompson’s group T and various generalizations of Thompson’s group V have global fixed points when they act semi-simply on finite-dimensional complete CAT(0) spaces, while it is known that T and V act properly on infinite-dimensional CAT(0) cube complexes.

scholarly journals Non-hyperbolic automatic groups and groups acting on CAT(0) cube complexes

2014 ◽  
Vol 24 (06) ◽  
pp. 795-813
Author(s):  
Yoshiyuki Nakagawa ◽  
Makoto Tamura ◽  
Yasushi Yamashita
Keyword(s):  
Cube Complex ◽  
Automatic Group ◽  
Mild Conditions ◽  
Automatic Groups ◽  
Cube Complexes

We discuss a problem posed by Gersten: Is every automatic group which does not contain ℤ × ℤ subgroup, hyperbolic? To study this question, we define the notion of "n-track of length n", which is a structure like ℤ × ℤ, and prove its existence in the non-hyperbolic automatic groups with mild conditions. As an application, we show that if a group acts freely, cellularly, properly discontinuously and cocompactly on a CAT(0) cube complex and its quotient is "weakly special", then the above question is answered affirmatively.

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