Shape of Data: Algebraic Topology and Shape Representation

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Related lectures (31)

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Chain Maps: Homotopy Invariance

Covers chain maps, homotopy invariance, homology groups, and induced homomorphisms between cycles and boundaries.

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Naturality: An Example

Covers the concept of naturality in algebraic topology and the generation of homology groups through induction.

Naturality: Chain Complexes and Homology Groups

Explores naturality in chain complexes, homology groups, and abelian groups, emphasizing the commutativity of squares and the Five-Lemma.

Topologie: Attachment Applications

Covers exercises on attaching 1-cells to intervals in topology.

Topology: Course Notes 2021

Covers course notes on topology, discussing Stasheff Mérida, cost-savings, and representative points.

Relative Homology: Homotopy Invariance

Explains relative homology, n-cycles, n-boundaries, and exact sequences of chain complexes.

Relative Homology: Exact Sequence

Covers the long exact sequence of relative homology groups and chain complexes.

Topological Data Science

Delves into Topological Data Analysis, emphasizing the mathematical foundations of neural networks and exploring the manifold hypothesis and persistent homology.

Cell Attachment and Homotopy

Covers cell attachment, homotopy, mappings, and universal properties in topology.