Cellular Homology: Applications

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Related lectures (31)

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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: Structure and Complexes

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

Hurewicz Theorem

Explores the proof of the Hurewicz Theorem and its applications to spheres and homotopy groups.

Excision Theory: Sketch of Proof

Outlines the proof of the excision theory using the barycentric subdivision.

Cell Attachment: Large Cell

Delves into cell attachment, exploring its implications for different cell dimensions.

Induced Homomorphisms on Relative Homology Groups

Covers induced homomorphisms on relative homology groups and their properties.

Simplicial and Singular Homology Equivalence

Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.

Simplicial Homology Revisited

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

Homotopy Invariance: Homology Groups

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

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.