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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747

The state sum invariant of 3–manifolds constructed from the E6 linear skein

Kenta Okazaki

Algebraic & Geometric Topology 13 (2013) 3469–3536

DOI: 10.2140/agt.2013.13.3469

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, E6 subfactor planar algebra, 3–manifolds, triangulation, linear skein

Mathematical Subject Classification

Primary: 57M15, 57M27

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/