CW Approximation Theorem

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Related lectures (31)

Page 3 of 4

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

Understanding Lifting Properties in Homotopy Theory

Focuses on lifting properties in homotopy theory of chain complexes.

Homotopy Theory of Chain Complexes

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

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.

Simplicial and Singular Homology Equivalence

Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.

Homology of Riemann Surfaces

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

Chain Maps: Homotopy Invariance

Covers chain maps, homotopy invariance, homology groups, and induced homomorphisms between cycles and boundaries.

Serre model structure: Left and right homotopy

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

Singular Homology: First Properties

Covers the first properties of singular homology and the preservation of decomposition and path-connected components in topological spaces.

Knot Theory: The Quadratic Linking Degree

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