- Days
- Tuesday, Wednesday (Tutorial) and Thursday
- Time
- 14:00–15:30
- Venue
- Room 228, Main Building
- Tutor
- Arnab Kundu
Schedule
Syllabus
- Categories, functors, and natural transformations. Review of homotopy and the definition of the fundamental group of a topological space.
- Free products of groups; the Seifert–Van Kampen theorem; covering spaces; the lifting criterion; existence of universal coverings; classification of covering spaces; and automorphisms of coverings.
- The Eilenberg–Steenrod axioms; Δ-complexes; simplicial homology; singular homology; the Mayer–Vietoris sequence; and the Jordan–Brouwer separation theorem.
- The universal coefficient theorem; the Künneth formula; CW complexes; cellular homology; and the Lefschetz fixed-point theorem.