07-1352/Class Notes for January 30

07-1352/Navigation Panel   Back to 06-1350 # Week of... Links 1 Jan 9 About, Notes 2 Jan 16 Notes 3 Jan 23 Notes 4 Jan 30 Notes and Plans 5 Feb 6 Notes 6 Feb 13 Notes R Feb 20 Reading week 7 Feb 27 Notes 8 Mar 6 Notes 9 Mar 13 Notes 10 Mar 20 Notes 11 Mar 27 Notes 12 Apr 3 Map 13 Apr 10 Dancso SP Apr 17 Chu, Sankaran, Amir-Khosravi Suggested Student Topics

In Preparation

The information below is preliminary and cannot be trusted! (v)

Tentative Future Plans

Today

• A discussion of grading policy.
• A bit more about quotients, and especially, some discussion of The HOMFLY Braidor Algebra.
• Ng's no-go theorem for ribbon knots (arXiv:q-alg/9502017 and arXiv:math.GT/0310074) and the no-go theorems we still don't have (and with a lot of luck, we'll never have) about the fusion number, the unknotting number and the genus.

The Following Two Weeks

• The construction of Z following Kontsevich's Knizhnik-Zamolodchikov approach with the added wisdom of [Le_Murakami_97] and [Murakami_Ohtsuki_97].

References

[Le_Murakami_97] ^  T. Q. T. Le and J. Murakami, Parallel Version of the Universal Vassiliev-Kontsevich Invariant, Journal of Pure and Applied Algebra 121 (1997) 271-291.

[Murakami_Ohtsuki_97] ^  J. Murakami and T. Ohtsuki, Topological Quantum Field Theory for the Universal Quantum Invariant, Communications in Mathematical Physics 188-3 (1997) 501-520.