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Fundamental GroupsExplores fundamental groups, homotopy classes, and coverings in connected manifolds.
Classification of ExtensionsExplores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.
Group CohomologyCovers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.
Group Actions on SetsExplores group actions on sets through homomorphisms and Cartesian products, illustrating their properties and equivalent definitions.
Seifert van Kampen: the pointFocuses on the Seifert van Kampen theorem, demonstrating an isomorphism between fundamental groups using a three-dimensional diagram.
Free Product: Group TheoryCovers the concept of the free product in group theory and how to determine monomorphisms and homomorphisms.
Recap of Group TheoryProvides a recap of group theory, defining a group as a set with a multiplication operation.