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**