MT4114 Algebraic Topology

Lectures

Monday 11:00-11:55

Tuesday 3:00-3:55 (Tutorials on alternate weeks)

Wednesday 11:00-11:55

Tutorials

Alternate Tuesdays 3:00-3:55

Weekly homework problems will be uploaded here.

Course contents

Review of quotient spaces.

Paths and homotopy, fundamental groups, the fundamental group of a circle. Covering spaces, lifting properties, classification of covering spaces, deck transformations. Free groups and free products, van Kampen theorem, applications to CW complexes.

Simplicial homology, singular homology, homotopy invariance, exact sequences, and excision. Degree, cellular homology, Mayer-Vietoris sequences, homology with coefficients. Axioms for homology.

References

1. M.A. Armstrong, Basic topology

2.  A. Hatcher, Algebraic topology

3. W.S. Massey, A Basic course in algebraic topology

4. J. Munkres, Topology

5. J. Munkres, Algebraic Topology

Evaluation

Quizzes: 40%

Mid-sem: 30%

End-sem: 30%