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A Jones polynomial for braid-like isotopies of oriented links and its categorification

Benjamin Audoux and Thomas Fiedler

Algebraic & Geometric Topology 5 (2005) 1535–1553

arXiv: math.GT/0503080

Abstract

A braid-like isotopy for links in 3–space is an isotopy which uses only those Reidemeister moves which occur in isotopies of braids. We define a refined Jones polynomial and its corresponding Khovanov homology which are, in general, only invariant under braid-like isotopies.

Keywords
braid-like isotopies, Jones polynomials, Khovanov homologies
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 20F36
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Publication
Received: 9 March 2005
Revised: 20 October 2005
Accepted: 24 October 2005
Published: 16 November 2005
Authors
Benjamin Audoux
Laboratoire E.Picard
Université Paul Sabatier
Toulouse
France
Thomas Fiedler
Laboratoire E.Picard
Université Paul Sabatier
Toulouse
France