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

Okazaki, Kenta

doi:10.2140/agt.2013.13.3469

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

The state sum invariant of $3$–manifolds constructed from the $E_6$ linear skein

Kenta Okazaki

Algebraic & Geometric Topology 13 (2013) 3469–3536

DOI: 10.2140/agt.2013.13.3469

Abstract

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

Volume 13, issue 6 (2013)