Tentative Schedule of Topics and Homework List

 
Date
Topic
Read
Exercises
Due
9/2
Introduction Section 1.1 Exercises 1.2, 1.5, 1.7
Show that the following is a projection of the right-handed trefoil:
9/9
9/4
Composition of Knots Section 1.2 Show that the figure-8 knot is amphichiral.
Exercises 1.8, 1.9
9/9
9/9
Reidemeister Moves Section 1.3 Demonstrate a sequence of Reidemeister moves and planar isotopies that show that the following projection is equivalent to the standard projection of the right-handed trefoil:
9/16
9/11
Links Section 1.4 Exercises 1.16, 1.17, 1.18
9/16
9/16
Tricolorability Section 1.5 Exercises 1.24, 1.25, 1.29
9/23
9/18
Knot Tabulation and the Dowker Notation for Knots Section 2.1
Section 2.2
Exercises 2.3, 2.6, 2.8
9/23
9/23
Conway's Notation Section 2.3 Exercises 2.10, 2.13, 2.14, 2.19, 2.21, 2.22
9/30
9/25
Unknotting Number Section 3.1 Exercises 3.2, 3.5, 3.6
9/30
9/30
Bridge Number and Crossing Number
Project 1
10/14
10/2
Surfaces without Boundary Section 3.2
Section 3.3
Section 4.1
Exercises 3,14, 4.2, 4.3
10/7
10/7
Surfaces without Boundary


10/9
Surfaces without Boundary
Exercises 4.10
10/14
10/14
Surfaces with Boundary Section 4.2 Exercises 4.14, 4.15, 4.16
Project 2
Homework: 10/21
Project: 10/23
10/16
Genus and Seifert Surfaces Section 4.3 Exercises 4.20, 4.22
10/23
10/21
Genus and Seifert Surfaces


10/23
The Seifert matrix and S-equivalence


10/30
The Alexander Polynomial


11/4
The Bracket Polynomial and the Jones Polynomial Section 6.1 Exercises 6.2, 6.5, 6.7
Extra Credit: Exercise 6.8
11/11
11/6
The Bracket Polynomial and the Jones Polynomial


11/11
The HOMFLY Polynomial Section 6.3
Section 6.4
Exercises 6.14, 6.18
11/18
11/13
Topology
Project 3
11/25
11/18
Higher Dimensional Knotting Chapter 10 Exercises 10.1, 10.2, 10.3 10.4
12/2
11/20
Higher Dimensional Knotting
Project 4
12/4
12/2
Legendrian Knots


12/4
Legendrian Knots