Contracting Subspaces

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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.

Homotopical Algebra: Introduction

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

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.

Model Categories and Homotopy Theory: Functorial Connections

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

Serre model structure on Top

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

Introduction to Model Categories

Explores lifting properties and model categories in topological spaces.

Serre model structure: Left and right homotopy

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

Universal Covering

Explores the concept of a universal cover of a topological space and the necessary conditions for a space to have one.