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On the universal sl2 invariant of Brunnian bottom tangles

Published online by Cambridge University Press:  01 October 2012

SAKIE SUZUKI
SAKIE SUZUKI*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan. e-mail: sakie@kurims.kyoto-u.ac.jp
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Abstract

The universal sl2 invariant is an invariant of bottom tangles from which one can recover the colored Jones polynomial of links. We are interested in the relationship between topological properties of bottom tangles and algebraic properties of the universal sl2 invariant. A bottom tangle T is called Brunnian if every proper subtangle of T is trivial. In this paper, we prove that the universal sl2 invariant of n-component Brunnian bottom tangles takes values in a small subalgebra of the n-fold completed tensor power of the quantized enveloping algebra Uh(sl2). As an application, we give a divisibility property of the colored Jones polynomial of Brunnian links.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 154 , Issue 1 , January 2013 , pp. 127 - 143
Copyright
Copyright © Cambridge Philosophical Society 2012

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