Lecture notes on Topology by Huynh Quang Vu

Lecture notes on Topology by Huynh Quang Vu

This note covers general topology, Geometric topology and differential topology.

Author(s): Huynh Quang Vu

118 Pages

General Topology by Paul Souverains

This note covers topological spaces, Continuous functions, Compact topological spaces, Compact metric spaces, Separability axioms and theorems, Metrizations.

Author(s): Paul Souverains

323 Pages

Topology I and II by Chris Wendl

This note describes the following topics: Metric spaces, Topological spaces, Products, sequential continuity and nets, Compactness, Tychonoff’s theorem and the separation axioms, Connectedness and local compactness, Paths, homotopy and the fundamental group, Retractions and homotopy equivalence, Van Kampen’s theorem, Normal subgroups, generators and relations, The Seifert-van Kampen theorem and of surfaces, Torus knots, The lifting theorem, The universal cover and group actions, Manifolds, Surfaces and triangulations, Orientations and higher homotopy groups, Bordism groups and simplicial homology, Singular homology, Relative homology and long exact sequences, Homotopy invariance and excision, The homology of the spheres, Excision, The Eilenberg-Steenrod axioms, The Mayer-Vietoris sequence, Mapping tori and the degree of maps, ocal mapping degree on manifolds Degrees, triangulations and coefficients, CW-complexes, Invariance of cellular homology.

Author(s): Chris Wendl

382 Pages

General Topology by Tom Leinster

This note covers the following topics: Topological spaces, metric spaces, Topological properties, Subspaces, Compactness, Compact metric spaces, Connectedness, Connected subsets of the real line.

Author(s): Tom Leinster

85 Pages