TRIANGLES, SQUARES AND GEODESICS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250041 ◽  
Author(s):  
RENA LEVITT ◽  
JON MCCAMMOND
Keyword(s):  
Nonpositive Curvature ◽  
Higher Dimensions ◽  
Fundamental Groups ◽  
Nonpositively Curved ◽  
Cube Complexes

In the early 1990s Steve Gersten and Hamish Short proved that compact nonpositively curved triangle complexes have biautomatic fundamental groups and that compact nonpositively curved square complexes have biautomatic fundamental groups. In this paper we report on the extent to which results such as these extend to nonpositively curved complexes built out a mixture of triangles and squares. Since both results by Gersten and Short have been generalized to higher dimensions, this can be viewed as a first step towards unifying Januszkiewicz and Świȧtkowski's theory of simplicial nonpositive curvature with the theory of nonpositively curved cube complexes.

Rigidity of nonpositively curved graphmanifolds

1986 ◽  
Vol 274 (1) ◽  
pp. 19-26 ◽  
Author(s):  
Viktor Schroeder
Keyword(s):  
Nonpositively Curved

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 Rigidity and characteristic classes of smooth bundles with nonpositively curved fibers

2016 ◽  
Vol 9 (3) ◽  
pp. 934-956
Author(s):  
Mauricio Bustamante ◽  
F. Thomas Farrell ◽  
Yi Jiang
Keyword(s):  
Characteristic Classes ◽  
Nonpositively Curved
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