Lecture

Topology: Lecture Notes 2021

Related lectures (41)

Topology: Disk Deprivation

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

Cell Attachment and Homotopy

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

Homotopy and Quotient Spaces

Covers homotopy, quotient spaces, and the universal property in topology.

Algebraic Kunneth Theorem

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Serre model structure on Top

Explores the Serre model structure on Top, focusing on right and left homotopy.

Base B for the covering

Explores constructing a base B for a topology using homotopy classes and paths.

Mapping Cylinders and Mapping Cones

Explores mapping cylinders and cones, key in exact sequences and topology.

Homotopy Classes

Covers the concept of homotopy classes and their properties in topology, including short components and group concatenation.

Topology: Fundamental Groups and Applications

Provides an overview of fundamental groups in topology and their applications, focusing on the Seifert-van Kampen theorem and its implications for computing fundamental groups.

Topology: Homotopy and Projective Spaces

Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.

Active Learning: Functors and Geometric Realization

Covers the computation of nerves and geometric realization in simplicial sets, along with functors into and out of the category of simplicial sets.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

The Topological Künneth Theorem

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

Homotopic Extension Problem

Explores solving the homotopic extension problem, constructing relative CW complexes, and ensuring uniqueness in CW approximations.

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.

Topological Scattering: From Graphs to Networks

Covers defining topological phases for photonic systems using unitary scattering matrices, transitioning from graphs to networks.

Topology: Open and Faded Subspace

Covers open and faded subspaces in topology with examples and exercises.

Homotopy Theory: Cylinders and Path Objects

Covers cylinders, path objects, and homotopy in model categories.

Topology: Course Notes 2021

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

Local structure of totally disconnected locally compact groups I

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