Knots can be studied from several points of view. Some of these points of view are more geometric, some more algebraic. We will consider knots from the point of view of geometric topology, as subsets of 3-dimensional spaces, more specifically, manifolds. The course will cover several topics related to this study. Sources for this course will include my book on 3-manifolds and Rolfsen's book on knots and links, among others.
1) My favorite 3-manifolds (definitions and examples)
2) Basic concepts in knot theory
3) The Kakimizu complex
4) Heegaard splittings
5) The curve complex
6) Other topics as time permits and inspiration strikes
Homework will be assigned related to each of the topics above. Homework will not be collected. One class period will be devoted to discussing the assigned homework for a given topic. Students will collect points for volunteering to discuss homework problems. (2 points for a perfect solution, one point for a reasonable attempt. 10 points = A, 8-9 points = A-, 7 points B+, 6 points = B, 5 points = B-, etc)