Unoriented topological quantum field theory and link homology

Turaev, Vladimir; Turner, Paul

doi:10.2140/agt.2006.6.1069

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Unoriented topological quantum field theory and link homology

Vladimir Turaev and Paul Turner

Algebraic & Geometric Topology 6 (2006) 1069–1093

DOI: 10.2140/agt.2006.6.1069

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

References

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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

Volume 6, issue 3 (2006)