Homology: Introduction and Applications

Related lectures (32)

Explores simplicial and singular homology, reduced homology groups, and their connection to the fundamental group.

Covers the quadratic linking degree in knot theory, exploring its definitions, properties, and significance in algebraic geometry.

Delves into applying cellular homology to compute homology groups and Euler characteristic, showcasing its practical implications.

Covers the concept of excision in algebraic topology with a focus on simplicial and singular homology.

Covers the structure of topological spaces with A-complexes and chain complexes.

Covers the proof of Theorem A, discussing homology, quotients, and isomorphisms.

Explores homotopy invariance and its application to homology groups of quotients, showcasing isomorphism and chain homotopy.

Explains cellular homology and the computation of homology groups using boundary maps.

Covers homology groups of quotients, homotopy invariance, and exact sequences.

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

Covers the concept of orientation and degrees in topology, focusing on assigning orientations to manifolds.

Covers linear independence, bases, and coordinate systems with examples and theorems.

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