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Abstract
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The
state sum invariant is a topological invariant of closed
–manifolds constructed
by using the –symbols
of the subfactor. In this
paper, we introduce the
linear skein as a certain vector space motivated by
subfactor planar algebra, and develop its linear skein theory by showing many relations
in it. By using this linear skein, we give an elementary self-contained construction of
the
state sum invariant.
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Keywords
state sum invariant, Turaev–Viro–Ocneanu invariant, $E_6$
subfactor planar algebra, $3$–manifolds, triangulation,
linear skein
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Mathematical Subject Classification 2010
Primary: 57M27, 57M15
Secondary: 46L37
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Publication
Received: 8 March 2013
Revised: 4 June 2013
Accepted: 6 June 2013
Published: 10 October 2013
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