scholarly journals Topological rigidity fails for quotients of the Davis complex

2018 ◽  
Vol 146 (12) ◽  
pp. 5357-5366
Author(s):  
Emily Stark
Keyword(s):  
Davis Complex

scholarly journals The fattened Davis complex and weighted L2–(co)homology of Coxeter groups

2016 ◽  
Vol 16 (4) ◽  
pp. 2067-2105 ◽  
Author(s):  
Wiktor Mogilski
Keyword(s):  
Coxeter Groups ◽  
Davis Complex

scholarly journals Automorphisms of Contact Graphs of CAT(0) Cube Complexes

2020 ◽  
Author(s):  
Elia Fioravanti
Keyword(s):  
Automorphism Group ◽  
Coxeter Groups ◽  
Universal Cover ◽  
Cube Complex ◽  
Contact Graph ◽  
Universal Covers ◽  
Davis Complex ◽  
Contact Graphs ◽  
Cube Complexes

Abstract We show that, under weak assumptions, the automorphism group of a $\textrm{CAT(0)}$ cube complex $X$ coincides with the automorphism group of Hagen’s contact graph $\mathcal{C}(X)$. The result holds, in particular, for universal covers of Salvetti complexes, where it provides an analogue of Ivanov’s theorem on curve graphs of non-sporadic surfaces. This highlights a contrast between contact graphs and Kim–Koberda extension graphs, which have much larger automorphism group. We also study contact graphs associated with Davis complexes of right-angled Coxeter groups. We show that these contact graphs are less well behaved and describe exactly when they have more automorphisms than the universal cover of the Davis complex.

Sign in / Sign up

Export Citation Format

Share Document