Lectures related to Homotopy Extension Property

Introduces the homotopy extension property, exploring conditions for extending continuous maps.

Explores the homotopy extension property for contractable subspaces and their quotient maps.

Covers the fundamentals of homotopy and its applications in topology.

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.

Homotopy Theory: Cylinders and Path Objects

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

Topology: Homotopy and Projective Spaces

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

Topology: Homotopy and Cone Attachments

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.

Homology of Riemann Surfaces

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

Topology: Fundamental Groups and Surfaces

Discusses fundamental groups, surfaces, and their topological properties in detail.

Knot Theory: The Quadratic Linking Degree

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

CW Complexes

Covers the construction and properties of CW complexes, including weak topology and characteristic maps.

Introduction to Model Categories

Explores lifting properties and model categories in topological spaces.

Induced Homomorphisms on Relative Homology Groups

Covers induced homomorphisms on relative homology groups and their properties.

Topology: Separation Criteria and Quotient Spaces

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Model Categories and Homotopy Theory: Functorial Connections

Covers the relationship between model categories and homotopy categories through functors preserving structural properties.

Exponential Law: Mapping Spaces and Compactness

Explores the exponential law for mapping spaces and the role of compactness in topological theory.

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.

Transformations and Inversions: Laplace and Fourier

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.

Homotopy Category of a Model Category

Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.

Spatial Topological Queries

Explores topology, test functions, and space operators for spatial queries.