Fundamental GroupsExplores fundamental groups, homotopy classes, and coverings in connected manifolds.
Homotopy IdentificationDelves into homotopy identification, pushout diagrams, colimits, and group fundamental calculations.
Group CohomologyCovers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Seifert van Kampen: the pointFocuses on the Seifert van Kampen theorem, demonstrating an isomorphism between fundamental groups using a three-dimensional diagram.
Concrete CategoriesCovers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.
Cohomology: Cross ProductExplores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Relative Homotopy GroupsCovers relative homotopy groups, establishing long exact sequences and defining boundary homomorphisms.