Introduction to knot theory (2015-16)


Course information:




March 15th, (1:30pm-4:30pm)
         Finite type invariants (definition, examples) ; chord diagrams, weight systems and the fundamental theorem

March 8th, (1:30pm-4:30pm)
         Properties of the Jones polynomial (orientation, miror image, skein relation, connected sum) and Tait conjecture ; Quantum invariants (Yang-Baxter equations and braid representations, enhanced Yang-Baxter operators and link invariants)

March 1st, (1:30pm-4:30pm)
         Milnor invariants (definition, example, properties) ; Jones polynomial (definition via Kauffman bracket)

Feb. 11th, 9am-12am
         Alexander polynomial (definition using the infinite cyclic cover, computation using Seifert matrices, properties, Alexander-Conway polynomial) ; Milnor invariants (definition)

Feb. 2nd, 1:30pm-4:30pm
        linking number (classification results) ; the knot group (def, case of torus knots, wirtinger presentation, Waldhausen theorem) ; matrix presentation and order of a module

Jan. 26th, 1:30pm-4:30pm
        braids ; Alexander theorem ; braid index ; Markov theorem ; linking number (equivalent definitions)

Jan. 19th, 2pm-5pm
        crossing number ; unknotting number ; Seifert surfaces ; knot genus

Jan. 12th, 2pm-4pm
        proof of the Reidemeister theorem ; the tricolorability invariant ; connected sum and the knot monoid

Jan. 12th, 10am-12am
        Definition of knots and knot equivalence ; polygonal knots and p-equivalence ; knot diagrams ; Reidemeister theorem



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