Cellular Homology: Applications

Related lectures (31)

Page 1 of 4

Explores the comparison of long exact sequences for vibrations and the relationship between homotopy and homology groups.

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Explores the CW Approximation Theorem, constructing CW complexes from spaces to ensure isomorphism on homology groups.

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Covers homology with coefficients, introducing the concept of defining homology groups with respect to arbitrary abelian groups.

Covers the first properties of singular homology and the preservation of decomposition and path-connected components in topological spaces.

Introduces homology as a tool to distinguish spaces in all dimensions and provides insights into its construction and applications.

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.