Algebraic
Topology

This is an Algebraic Topology course for students in Semester III of the M.Sc. Mathematics programme at HRI, offered from August to December 2026.

Schedule

Days
Tuesday, Wednesday (Tutorial) and Thursday
Time
14:00–15:30
Venue
Room 228, Main Building
Tutor
Arnab Kundu

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.
Detailed syllabus  ↗

Assignments