Cube Complexes and Finiteness Properties of Block Mapping Class Groups

Explore a lecture on using cube complexes to understand finiteness properties of block mapping class groups. Delve into joint research that defines a new family of subgroups within the mapping class group of a surface with a Cantor set removed. Learn how these "Block Mapping Class Groups" are constructed using tree-like surfaces and homeomorphisms with specific preservation properties. Discover the connection between these groups and Thompson's groups, and understand their finiteness properties in relation to subgroups of surface mapping class groups. Examine the construction of subgroups with specific finiteness properties and their containment of mapping class groups of compact surfaces. Gain insights into the application of cube complexes, particularly the Stein-Farley cube complex, in analyzing these groups and their properties.