ON STOCHASTIC COSURFACES AND TOPOLOGICAL QUANTUM FIELD THEORIES
Résumé
We analyze the notion of a stochastic cosurface and show the following: the obstructions to the construction of non-abelian stochastic cosurfaces previously highlighted can be overcome by an ordering choice; the presence of an underlying manifold is not mandatory and stochastic cosurfaces can be defined in more general CW-complexes. We also describe a dimension extension procedure, in which any d-stochastic cosurface can be extended to a (d + k)-stochastic cosurface if the underlying CW-complex has (d + k)-faces. We finish with a link of stochastic cosurfaces with topological quantum field theories and with an analog of deformation algebra indexed by a non-linear set of formal variables.