1. Knot groups

( Wirtinger presentation, Knot groups of torus knots, unknotting theorem, knot group of composite knots, prime knots are determined by their knot groups )

 

2. Linking number

( Definition of linking number by Gauss, homological and combinatorial definitions, and their equivalences )

 

3. Genus

 

4. Connected sum of knots

( Prime and composite knots, unique decomposition theorem, additive property of the genus of connected sum of knots, non-cancelation theorem )

 

5. Alexander - Conway polynomial

( Seifert surface, Seifert matrix, construction of Alexander-Conway polynomial, skein relation of Conway )

 

6. Jones polynomial

( Braids and braid groups, Alexander theorem, Markov theorem, Hecke algebra, Ocneanu trace theorem, Jones' original construction of his polynomial, skein relation, two variable Jones polynomial and its properties, Kauffman bracket )

 

Registration

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