Homology: Introduction and Applications

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Related lectures (31)

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Topology: Disk Deprivation

Delves into disk deprivation in topology, showcasing how spaces emerge from this process.

Topology Seminar: Tower Sequences and Homomorphisms

Explores tower sequences, homomorphisms, and their applications in topology, including the computation of homology and the construction of telescopes.

Simplicial Homology Revisited

Covers the concept of simplicial homology, focusing on finite complexes and induced maps.

Homology and the fundamental group

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

Knot Theory: The Quadratic Linking Degree

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

Cellular Homology: Applications

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

Excision: An Example

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

Simplicial Homology: Structure and Complexes

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

EML Spaces and Cohomology

Covers spaces, homology, chain groups, and abelianization in CW complexes and maps.

Homology Theorem

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