Communications in Mathematical Physics

, Volume 151, Issue 2, pp 355–402 | Cite as

A combinatorial approach to topological quantum field theories and invariants of graphs

  • M. Karowski
  • R. Schrader


The combinatorial state sum of Turaev and Viro for a compact 3-manifold in terms of quantum 6j-symbols is generalized by introducing observables in the form of coloured graphs. They satisfy braiding relations and allow for surgeries and a discussion of cobordism theory. Application of these techniques give the dimension and an explicit basis for the vector space of the topological quantum field theory associated to any Riemann surface with arbitrary coloured punctures.


Colour Neural Network Statistical Physic Vector Space Complex System 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • M. Karowski
    • 1
  • R. Schrader
    • 1
  1. 1.Institut für Theoretische PhysikFreie Universität BerlinBerlin 33Germany

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