Lectures related to Homotopy Extension Property

Induced Homomorphisms on Relative Homology Groups

Covers induced homomorphisms on relative homology groups and their properties.

Topology: Homotopy and Projective Spaces

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

Demonstrates how to obtain homotopy equivalences between different spaces using the homotopy extension property.

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

Homotopy: Fundamentals and Examples

Covers the fundamentals of homotopy and its applications in topology.

Contracting Subspaces

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

Topology: Fundamental Groups and Surfaces

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

Homotopy Theory: Cylinders and Path Objects

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

Knot Theory: The Quadratic Linking Degree

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

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 Invariance

Explores homotopy invariance, emphasizing the preservation of properties under continuous functions and their relationship with topological spaces.

Manifolds: Charts and Compatibility

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

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.

Homotopical Algebra: Introduction

Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.

Homology of Riemann Surfaces

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

Model Categories: Properties and Structures

Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.

Dimension Theory: Topological Space and Closed Subsets

Explores dimension theory in topological spaces and closed subsets, including height interpretation and additivity.

CW Pairs: Homotopy Extension Property

Discusses how CW pairs satisfy the homotopy extension property through retractions and homotopy extension properties.