Topology II

Instructor: Amritanshu Prasad      Room 217; Mondays and Thursdays at 9:30am.

Grading scheme

There will be one homework assignment every week, due before class the following Monday. Four randomly selected problems will be corrected. There will be a mid-semester exam and a final exam. The aggregate score will be computed giving homework a weight of 30%, mid-semester exam a weight of 20%, and final exam a weight of 50%. Letter grades will be determined as follows:
Grade A: 90 - 100
Grade B: 80 - 89
Grade C: 70 - 79
Grade D: 60 - 69
Grade F: 0 - 59
Final Exam.

Homework

Listed by due date
January 11, 18, 25.
February 1, 15, 22.
March 16, 29.

Topics covered

4th January: categories, functors, groupoids, simplicial complexes.
11th January: geometric realization, chain complexes.
18th January: simplicial homology of a simplicial complex, singular homology of a topological space.
21st January: chain homotopy.
25th January: acyclic models.
28th January: acyclic models (continued), augmented chain complexes.
1st February: acyclic models for augmented chain complexes.
4th February: coning on chain complexes, ordered chain complex of a simplicial complex.
8th February: natural equivalence of ordered and oriented chain complexes, direct limits.
11th February: homology commutes with direct limits.
15th February: Homotopic functions induce chain homotopic maps of singular chain complexes, computation of singular 0th homology.
18th February: Subdivision of a singular chain complex.

References

  1. Algebraic Topology, by E. H. Spanier.