Instructor: Yu Pan Office 2-177 Email: yupan[at]mit.edu Office hour: By appointment Writing Instructor: Malcah Effron Email: meffron[at]mit.edu Time: MWF 10-11 Location: 2-151
Textbook:
Knot Theory and its applications by Kunio Murasugi Knots and Links by Dale Rolfsen Other reference: Knot Theory by Charles Livingston. Knots, Links, Braids and 3-Manifolds by V.V. Prasolov and A. B. Sossinsky. The knot book by Colin Adams. An Introduction to Knot Theory by Raymond Lickorish.
Please find the course policy here.
Schedule: | Week | Date | Topics | Sections | Presenters | | 1 | Feb. 6 | Introduction to the course | | | | | Feb. 8 | Introduction to Knots theory | Roberts 1 | Pan | | 2 | Feb. 11 | Formal definitions | Roberts 2.1-2.2 | Varkey, Julian | | | Feb. 13 | Reidemeister Moves | Roberts 2.3 | Kaarel, Torri | | | Feb. 15 | Unknotting number | Roberts 3.2 | Earth, Dave | | 3 | Feb. 19 | Linking number | Murasugi 4.5 | Bau, | | | Feb. 20 | 3-coloring | Roberts 3.3 | Leon, Olga | | | Feb. 22 | p-coloring | Roberts 3.4 | Dylan, Kevin | | 4 | Feb. 25 | Alexander Polynomial | Roberts 3.5 | Earth, Bau | | | Feb. 27 | Problem Seminar | | | | | Mar. 1 | Review of fundamental group | Roberts 8.2 | Torri, Julian | | 5 | Mar. 4 | Van Kampen's Theorem | Roberts 8.3 | Varkey, Dave | | | Mar. 6 | Knot fundamental group | Roberts 8.4 | Leon, Olga | | | Mar. 8 | Problem seminar | | | | 6 | Mar. 11 | Seifert Surface | Roberts 7.1 | Kevin, Dylan | | | Mar. 13 | Genus of knots | Roberts 7.2 | Kaarel, | | | Mar. 15 | The Seifert Matrix | Murasugi 5.3 | | | 7 | Mar. 18 | S-equivalence (I) | Murasugi 5.4 | | | | Mar. 20 | S-equivalence (II) | Murasugi 5.4 | | | | Mar. 22 | Problem seminar | | | | 8 | | Spring Break | | | | 9 | Apr. 1 | Alexander Polynomial | Murasugi 6.1 | | | | Apr. 3 | Introduction to homology | | | | | Apr. 5 | Cyclic covering | Rolfsen 5C | | | 10 | Apr. 8 | Calculation on k-torsion | Rolfsen 6B | | | | Apr. 10 | Problem Seminar | | | | | Apr. 12 | Infinite Covering | Rolfsen 7A | | | 11 | Apr. 15 | Holiday | | | | | Apr. 17 | Seifert Surface again | Rolfsen 7B | | | | Apr. 19 | Writing Seminar | | | | 12 | Apr. 22 | Problem Seminar | | | | | Apr. 24 | Conway polynomial | Murasugi 6.2 | | | | Apr. 26 | Properties | Murasugi 6.3 | | | 13 | Apr. 29 | Writing Seminar | | | | | May 1 | Signature | Murasugi 6.4 | | | | May 3 | Problem Seminar | | | | 14 | May 6 | Presentations | | | | | May 8 | Presentations | | | | | May 10 | Presentations | | | | 15 | May 13 | Presentations | | |
Problem sets: |
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