Effective Rank-Rigidity in CAT(0) Cube Complexes

Effective Rank-Rigidity in CAT(0) Cube Complexes

Explore a lecture on effective rank-rigidity in CAT(0) cube complexes presented by Abdul Zalloum at the Workshop on Cube Complexes and Combinatorial Geometry. Delve into recent research that builds upon Caprace and Sageev's rank-rigidity theorem, examining how CAT(0) cube complexes with factor systems determine an integer m(X) that influences the structure of groups acting freely and cocompactly on the complex. Investigate the uniform application of flipping and skewering tools, and understand how these techniques can be accomplished quickly based on the geometry of the underlying cube complex. Gain insights into the conditions under which groups are either quasi-isometric to a product or contain rank-one elements of bounded length.