Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Explores the comparison of long exact sequences for vibrations and the relationship between homotopy and homology groups.
Explores the CW Approximation Theorem, constructing CW complexes from spaces to ensure isomorphism on homology groups.
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Explores the proof of the Hurewicz Theorem and its applications to spheres and homotopy groups.
Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.
