Unoriented topological quantum field theory and link homology

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.

This is the version published by Algebraic & Geometric Topology on 24 August 2006

References in corpus (4)

• Khovanov's homology for tangles and cobordisms
• On Khovanov's categorification of the Jones polynomial
• Categorification of the Kauffman bracket skein module of I-bundles over surfaces
• An invariant of link cobordisms from Khovanov homology

Cited by in corpus (16)

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• Virtual Khovanov homology using cobordisms
• Khovanov homology for virtual tangles and applications
• Moduli spaces of Klein surfaces and related operads
• Cyclic Foam Topological Field Theories
• Orientation twisted homotopy field theories and twisted unoriented Dijkgraaf-Witten theory
• Klein Topological Field Theories from Group Representations
• Diagrammatic State Sums for 2D Pin-Minus TQFTs
• Unoriented HQFT and its underlying algebra
• A mixed invariant of non-orientable surfaces in equivariant Khovanov homology
• Computations of the slice genus of virtual knots
• A Khovanov type invariant derived from an unoriented HQFT for links in thickened surfaces
• Invariants of r-spin TQFTs and non-semisimplicity
• Ascent concordance
• Symmetric monoidal equivalences of topological quantum field theories in dimension two and Frobenius algebras