Explore a 53-minute lecture on cubespaces and homotopy theory presented by Freddie Manners from the University of California at San Diego during the Simons Semester on Dynamics conference "Nilpotent structures in topological dynamics, ergodic theory and combinatorics." Delivered at the Będlewo Mathematical Research and Conference Center of the Institute of Mathematics of the Polish Academy of Sciences on June 8, 2023, delve into advanced mathematical concepts connecting geometric structures with topological principles.