Shape of Data: Algebraic Topology and Shape Representation

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Group Cohomology

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

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, including path object construction and fibrations.

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.

Homology Groups: Basics

Introduces reduced homology groups and explains their properties and applications in topology.

Orientation and degrees

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

Homology of Riemann Surfaces

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

Introduction to Topology

Covers fundamental concepts of space, topology, groups, and homology theory.

Topology: Classification of Surfaces and Fundamental Groups

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

The Topological Künneth Theorem

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

Homology: Introduction and Applications

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