MAT 326: Algebraic Topology

Instructor: Samuel Grushevsky
Topics:
De Rham cohomology, homotopy, manifolds, Poincare duality, bundles(?), cell complexes(?).

Textbook:
Madsen, I.H. and Tornehave, J.: From Calculus to Cohomology

Assignments: Weekly problem sets.

Take Home Final Exam: 40%
Weekly Problem Sets: 60%

Suggested preparation: some analysis, some algebra.

Schedule: 12:30 pm - 1:20 pm M W F
Classroom: Fine 1001

Homeworks: (in the book, starting on page 243)
Due September 20: 1.1, 1.2
Due September 27: 2.2, 2.3, 2.5, 2.8, 2.9, 2.11, 3.2, 3.3
Due October 4: 4.1, 4.3, 4.4, 5.3, 5.4
Due October 11: 6.3, 6.4, 6.5, 7.1, 7.2; Problem A: Use Mayer-Vietoris to compute the cohomology groups of the torus T=S^1\times S^1
Due October 18: 7.5, 8.2, 8.4, 8.5, 8.6; Problem A: Let D^3\subset R^3 be the (closed) unit ball, and let I be the segment [-1,1] on the x-coordinate axis in R^3. Let X be the union of I and the complement of D^3 in R^3. Is X a smooth manifold? Is it homotopy equivalent to a smooth manifold? Compute H^*(X)
Due November 6: 9.2, 9.3, 9.4, 9.9, 9.10, 9.13, 9.15, 9.16, 9.18
Due November 10: 10.5, 10.8, 10.11, 10.12, 10.14 (in 10.14 the first integral on the right should be over R, not the boundary; when the book says "Lebesque measure", it just means the volume form on R^n)
Due November 17: 11.4, 11.6, 11.11, 12.3, 12.5, 12.7, 12.8
Due December 1: 12.9, 12.11, 13.3, 13.5, 13.6, 13.9
Due December 8: 14.2, 14.3, 14.7, 15.4, 15.9, 15.12, 15.13
Due December 15: PDF
Take-home final (pdf)