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2005 Skein theory for $SU(n)$–quantum invariants
Adam S Sikora
Algebr. Geom. Topol. 5(3): 865-897 (2005). DOI: 10.2140/agt.2005.5.865


For any n2 we define an isotopy invariant, Γn, for a certain set of n–valent ribbon graphs Γ in 3, including all framed oriented links. We show that our bracket coincides with the Kauffman bracket for n=2 and with the Kuperberg’s bracket for n=3. Furthermore, we prove that for any n, our bracket of a link L is equal, up to normalization, to the SUn–quantum invariant of L. We show a number of properties of our bracket extending those of the Kauffman’s and Kuperberg’s brackets, and we relate it to the bracket of Murakami-Ohtsuki-Yamada. Finally, on the basis of the skein relations satisfied by n, we define the SUn–skein module of any 3–manifold M and we prove that it determines the SLn–character variety of π1(M).


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Adam S Sikora. "Skein theory for $SU(n)$–quantum invariants." Algebr. Geom. Topol. 5 (3) 865 - 897, 2005.


Received: 23 July 2004; Accepted: 9 May 2005; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1087.57008
MathSciNet: MR2171796
Digital Object Identifier: 10.2140/agt.2005.5.865

Primary: 57M27
Secondary: 17B37

Rights: Copyright © 2005 Mathematical Sciences Publishers


Vol.5 • No. 3 • 2005
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