In this course we deal with basic algebraic topology, focusing on homology and cohomology. Topics includes: singular and simplicial homology, homotopy, excision, Mayer-Vieotoris sequence, CW-complexes, applications of homology theory, cohomology, products, universal coefficient and Kunneth theorems, manifolds and Poincare duality.

It is required to have undergraduate-level backgrounds in general topology (topics in MATH 421; not including covering spaces and fundamental groups) and basic algebra (topics on abelian groups in MATH 301).

HW 20%
Mid 35%
Final 45%

The lectures will be based, but not entirely, on

- A. Hatcher, Algebraic topology, Cambridge University Press, 2002

This book is available, for free, from the author's website: http://www.math.cornell.edu/~hatcher/AT/ATpage.html

Also, parts of the following books will be often used.

- J. R. Munkres, Elements of algebraic topology, Addison-Wesley, 1984
- J. W. Vick, Homology theory, Academic Press, 1973
- M. J. Greenberg and J. R. Harper, Algebraic topology: a first course, Benjamin-Cummings, 1981
- J. Davis and P. Kirk, Lecture notes in algebraic topology, American Mathematicsl Society, 2001

We will cover the topics listed above, and the pace will be adjusted depending on students' performance. The expected schedule is as follows:
Week 1-2 Singular homology, homotopy invariance
Week 3-4 Excision, Mayer-Vieotoris sequence
Week 5-7 CW-complexes, cellular homology, and axioms of homology theory
Week 8 Midterm Exam
Week 9 Some applications of homology theory
Week 10 Singular and cellular cohomology
Week 11-12 Universal coefficient and Kunneth theorems
Week 13-14 Introduction to duality of manifolds
Week 16 Final Exam