The following is a tentative syllabus for the course.
Week | Lectures | Sections in Text | Brief Description | |
---|---|---|---|---|
1 | 3/30 | Ch. 1 Sec, 2.1 - 2.2 |
Introduction, history, and definitions of knots | |
4/1 | 2.3 - 3.1 | Equivalence of knots, Reidemeister moves | ||
4/3 | 3.2 - 3.3 | Colorings of knots | ||
2 | 4/6 | 3.3 - 3.4 | Generalizations of colorability | |
4/8 | 3.5 | The Alexander polynomial | ||
4/10 | 4.1 | Surfaces | ||
3 | 4/13 | 4.2 | Classification of surfaces | |
4/15 | 4.3 | Seifert surfaces and knot genus | ||
4/17 | 4.4 - 4.5 | Connected sums and prime decomposition, relations to invariants |
||
4 | 4/20 | 5.1 | Definition of a group, symmetric groups | |
4/22 | 5.2 - 5.3 | Labelling knots with symmetric groups | ||
4/24 | 5.4 | The group of a knot | ||
5 | 4/27 | 6.1 - 6.2 | Seifert matrices | |
4/29 | 6.2 | The Alexander polynomial, part 2 | ||
5/1 | Midterm Exam | Material covered from Chapters 1-5. | ||
6 | 5/4 | 6.3, 7.1 | The knot signature and other knot invariants | |
5/6 | 7.2 - 7.3 | New invariants, braids, and bridges | ||
5/8 | 7.4 - 7.5 | Relationships and independence of invariants | ||
7 | 5/11 | 10.1 | The Conway polynomial | |
5/13 | 10.2 | The Bracket polynomial | ||
5/15 | 9.1 | Higher-dimensional knots | ||
8 | 5/18 | 9.2 | Three dimensions from a 2-dimensional perspective | |
5/20 | 9.3 | Four dimensions from a 3-dimensional perspective | ||
5/22 | 9.4 | Slice knots | ||
9 | 5/25 | Memorial Day: no classes | ||
5/27 | 9.4 - 9.5 | The knot concordance group, part 1 | ||
5/29 | 9.5 | The knot concordance group, part 2 | ||
10 | 6/1 | |||
6/3 |