Table of Contents
ISRN Geometry
Volume 2014, Article ID 321509, 9 pages
Research Article

The Singular Temperley-Lieb Category

Department of Mathematics, California State University, Fresno, CA 93740, USA

Received 24 October 2013; Accepted 10 December 2013; Published 24 April 2014

Academic Editors: S. Hernández, S. Jafari, S. Kamada, and V. Roubtsov

Copyright © 2014 Carmen Caprau and Joel Smith. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce and study the singular Temperley-Lieb category over , which is a free pivotal category over two self-dual generators and is an extension of the (classical) Temperley-Lieb category. Our construction is motivated by a state model for the polynomial of an oriented link and provides a categorical perspective to this link invariant. We also construct a couple of polynomial invariants for oriented tangles from category theory point of view.