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Abstract
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The universal
invariant of bottom tangles has a universality property for the colored Jones
polynomial of links. A bottom tangle is called boundary if its components admit
mutually disjoint Seifert surfaces. Habiro conjectured that the universal
invariant of boundary bottom tangles takes values in certain subalgebras
of the completed tensor powers of the quantized enveloping algebra
of the Lie
algebra .
In the present paper, we prove an improved version of Habiro’s conjecture. As an
application, we prove a divisibility property of the colored Jones polynomial of
boundary links.
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Keywords
quantum invariant, universal invariant, colored Jones
polynomial, boundary link, bottom tangle
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M25
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Publication
Received: 2 April 2011
Revised: 1 February 2012
Accepted: 29 November 2011
Published: 7 May 2012
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