MAT 215C Syllabus

Textbook:
Algebraic Topology by Allen Hatcher.

Prerequisites:
MAT 215B; or Consent of Instructor.


Suggested Schedule:





Lectures (approx) Sections (from Hatcher's book)
Lecture 1&2
Informal definition of cohomology, examples
Lectures 3&4
Hom( ,G), exactness, Ext
Lecture 5
Universal Coefficient Theorem
Week 3
Quiz I

Properties of cohomology;
homotopy invariance, sequences of pairs and triples
Week 4-5 § 3.2 Cup products, properties, examples
Quiz II
Week 6-7 § 3.3 Homological manifolds, orientations, cap products
Poincare duality
Quiz III
Weeks 8-9 Student presentations
Quiz IV
Week 10 § 3.3 (continued) Other forms of duality


Additional Notes:
Other references:
  • Differential Forms in Algebraic Topology by R. Bott and L. Tu