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2017 NCTS Summer Course on Introduction to Knot Theory
14:00-16:00 on 7/10 (Mon.), 7/12 (Wed.), 7/14 (Fri.), 7/17 (Mon.), 7/19 (Wed.), 7/21 (Fri.), July 10 - 21, 2017
Room 440, Astronomy-Mathematics Building, NTU

Jih-Hsin Cheng (Academia Sinica)
C. Michael Tsau (Saint Louis University)
Mao-Pei Tsui (National Taiwan University)

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 )

Contact: Risa, 02-3366-8811, risalu@ncts.ntu.edu.tw

Poster: events_3_93170602295772189.jpg

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 (C) 2018 National Center for Theoretical Sciences