Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.
Provides a recap of group theory, defining a group as a set with a multiplication operation.
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Explores group actions on sets through homomorphisms and Cartesian products, illustrating their properties and equivalent definitions.
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
