The Singular Temperley-Lieb Category. (24th April 2014)

• Record Type: Journal Article
• Authors: Caprau, Carmen; Smith, Joel
• Other Names: Hernández S. Academic Editor.; Jafari S. Academic Editor.; Kamada S. Academic Editor.; Roubtsov V. Academic Editor.
• Is Part Of: ISRN geometry. Volume 2014(2014)
• Publication Date: 2014-04-24
• Subjects: Geometry -- Periodicals; Topology -- Periodicals; Geometry; Topology; Periodicals; 516
• DOI: 10.1155/2014/321509
• Languages: English
• ISSNs: 2090-6307

Abstract

Abstract : We introduce and study the singular Temperley-Lieb category overℤ [ q, q - 1 ], 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 thes l ( 2 ) 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.