Open AccessFor a fixed Turaev shadow Jones-Vassiliev invariants depend polynomially on the gleams
Author(s) -
Jens Lieberum
Publication year - 1997
Publication title -
commentarii mathematici helvetici
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.603
H-Index - 46
eISSN - 1420-8946
pISSN - 0010-2571
DOI - 10.1007/pl00000362
Subject(s) - mathematics , combinatorics , order (exchange) , polynomial , invariant (physics) , discrete mathematics , mathematical analysis , mathematical physics , finance , economics
. We use Turaev's technique of shadows and gleams to parametrize the set of all knots in S 3 with the same Hopf projection. We show that the Vassiliev invariants arising from the Jones polynomial J t (K) are polynomials in the gleams, i.e., for , the n-th order Vassiliev invariant u n , defined by , is a polynomial of degree 2n in the gleams.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom