Algebraic L theory and Topological Manifolds

General Topology lecture notes

This note covers introduction, Set theory, Topological spaces, Metric topologies, Connected spaces, Compactness, Advanced material.

Author(s): Thomas Baird

59 Pages

Introduction to Topology by Alex Kuronya

This note covers Basic concepts, Constructing topologies, Connectedness, Separation axioms and the Hausdorff property, Compactness and its relatives, Quotient spaces, Homotopy, The fundamental group and some applications, Covering spaces and Classification of covering spaces.

Author(s): Alex Kuronya

102 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