Math 526: Topology II

Algebraic Topology and Low Dimensional Topology

Instructor: Constance Leidy
Time: Tuesdays and Thursdays 10:30-11:50am
Location: Exley Science Center 618
Office: Science Tower 641
Office Hours: Mondays and Wednesdays 3:00-4:00pm and by appointment
Phone Number: 860-685-2435
E-Mail Address: cleidy@wesleyan.edu

Course Description

This course will discuss important concepts in algebraic topology such as homology, cohomology, and duality, and then introduce homology with local coefficients. The course will focus on examples from low-dimensional topology such as knots and 3-manifolds to illustrate the importance of these algebraic invariants.


References

If you decide to buy one book for this course, I would suggest buying Lecture Notes in Algebraic Topology by James F. Davis and Paul Kirk. It is available directly from the AMS or from the campus bookstore.

Another book which is a good reference for the basics of algebraic topology is Algebraic Topology by Allen Hatcher. It is available to download here, however it's probably worth the price to buy it already printed and bound from the campus bookstore.

If you want to learn more about knots and 3-manifolds, here are some good books to check out:

  • Knots and Links by Dale Rolfsen
  • Knots, Links, Braids and 3-Manifolds by Prasolov and Sossinksky
  • 3-manifolds by John Hempel

    A goal for the end of this course is to discuss some of the results in the following papers:

  • T. Cochran, Noncommutative knot theory
  • C. Leidy, Higher-order linking forms for knots

    Another (perhaps lofty) goal is to discuss some of the results in the following paper:

  • T. Cochran, S. Harvey, C. Leidy, Knot Concordance and Higher-Order Blanchfield Duality