An Invitation to the Lifting Decomposition in CAT(0) Cube Complexes

Explore the lifting decomposition associated with consistent half-spaces in CAT(0) cube complexes in this 49-minute lecture by Talia Fernos. Delve into the extension of previous work by Caprace and Sageev, addressing a question posed by Wise. Examine the simplicity and utility of this tool through various natural objects in CAT(0) cube complexes and the theorems they help prove. Discover recent collaborative research with Futer and Hagen, connecting different boundaries and roughly equipping the Tits boundary of a CAT(0) cube complex X with an Aut(X) equivariant simplicial structure. This talk, part of the Workshop on Cube Complexes and Combinatorial Geometry, offers valuable insights into advanced mathematical concepts and their applications.