Volume 6, issue 3 (2006)

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Unoriented topological quantum field theory and link homology

Vladimir Turaev and Paul Turner

Algebraic & Geometric Topology 6 (2006) 1069–1093

arXiv: math.GT/0506229

Abstract

We investigate link homology theories for stable equivalence classes of link diagrams on orientable surfaces. We apply (1+1)–dimensional unoriented topological quantum field theories to Bar-Natan’s geometric formalism to define new theories for stable equivalence classes.

Keywords
Khovanov homology, virtual link, stable equivalence, unoriented topological quantum field theory
Mathematical Subject Classification 2000
Primary: 57M25, 57R56
Secondary: 81T40
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Publication
Received: 1 September 2005
Revised: 16 January 2006
Accepted: 2 May 2006
Published: 24 August 2006
Authors
Vladimir Turaev
Institut de Recherche Mathématique Avancée
7 rue René Descartes
67000 Strasbourg
France
Paul Turner
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh EH14 4AS
Scotland