Volume 13, issue 6 (2013)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The state sum invariant of $3$–manifolds constructed from the $E_6$ linear skein

Kenta Okazaki

Algebraic & Geometric Topology 13 (2013) 3469–3536
Abstract

The E6 state sum invariant is a topological invariant of closed 3–manifolds constructed by using the 6j–symbols of the E6 subfactor. In this paper, we introduce the E6 linear skein as a certain vector space motivated by E6 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 E6 state sum invariant.

Keywords
state sum invariant, Turaev–Viro–Ocneanu invariant, $E_6$ subfactor planar algebra, $3$–manifolds, triangulation, linear skein
Mathematical Subject Classification 2010
Primary: 57M27, 57M15
Secondary: 46L37
References
Publication
Received: 8 March 2013
Revised: 4 June 2013
Accepted: 6 June 2013
Published: 10 October 2013
Authors
Kenta Okazaki
Research Institute for Mathematical Sciences
Kyoto University
Kyoto-shi 606-8502
Japan
http://www.kurims.kyoto-u.ac.jp/~junes/