Syllabus
- Homotopy and homotopy type,
- Cell complexes,
- Fundamental group,
- Van Kampen's theorem,
- Covering spaces,
- Classification of covering spaces, deck transformation group,
- Singular homology, simplicial homology,
- Exact sequences and excision,
- Equivalence of simplicial and singular homology,
- Mayer-Vietoris sequence,
- Cellular homology,
- Axioms for homology.
Annotation
Foundations of homotopy and singular homology theories. CW-complexes and their homology.
Basic cohomology theory. Applications.