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Related lectures (16)
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Abélianization: Fundamental Groups
Explores abélianization of fundamental groups in commutative spaces with examples and proofs.
Permutations and Symmetric Groups
Covers symmetric groups, transpositions, sign of a permutation, and conjugacy classes in permutations.
Symmetric Group and Alternating Group
Explores the Symmetric group, cycle notation, multiplication, the sign of a permutation, and the Alternating group.
Symmetric Group and Group Actions
Covers the Symmetric group, cycle decomposition, transpositions, even and odd permutations, and group actions.
Symmetric Group and Cycle Decomposition
Explores the Symmetric group, cycle decomposition, Orbit-Stabilizer theorem, and properties of cycles and transpositions.
Abelianization of Fundamental Group
Explores abelianization examples, homomorphisms, and isomorphisms in group theory.
Multilinear Forms: Notation & Applications
Covers multilinear forms in n variables over a k-vector space, emphasizing notation and applications.
EML Spaces and Cohomology
Covers spaces, homology, chain groups, and abelianization in CW complexes and maps.
Group Theory: Part 2
Delves into advanced group theory concepts such as isomorphisms and homomorphisms.
Multilinear Forms: Alternating and Symmetric
Covers alternating and symmetric multilinear forms in vector spaces over a field.
Algebra: Group Actions and Direct Products
Covers group actions, conjugacy classes, centralizers, direct products, and finite abelian groups.
Mayer-Vietoris Sequence
Explores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.
Nilpotent Lie Groups
Covers the properties of nilpotent Lie groups and the construction of non-degenerate alternating 2-forms.
Automorphism groups of trees and graphs
Explores automorphisms of graphs, focusing on automorphism groups, Cayley-Abels graphs, and quasi-isometry.
Topology: Classification of Surfaces and Fundamental Groups
Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.
Quotients in Abelian Groups
Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.
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