NPC cube complexes

Wednesday, May 17, 2017
Ora Inizio: 
16:30
Ora Fine: 
17:30
Leone Slavich
Università di Pisa

Cube complexes are analogues of simplicial complexes built using cubes
rather than simplices. Under very mild combinatorial assumptions, they
exhibit interesting geometric properties which make them useful in
studying the fundamental groups of negatively curved spaces such as
hyperbolic manifolds.
In the talk I will introduce them and review the theory behind them. In
particular I will show some techniques which allow to realize the
fundamental group of hyperbolic 3-manifolds as fundamental group of a
non-positively curved cube complex. If time allows, I will show the
application of this construction to the proof of the virtual fibering
conjecture.