Geometrical-topological correlation in structures

The topology of polyhedra, tessellations and networks is described as to their mapping in Schlaefli space. A description of the topological form index is given and it is applied to these structural classes in terms of their geometries

Fusion Residues

We discuss when and how the Verlinde dimensions of a rational conformal field theory can be expressed as correlation functions in a topological LG theory. It is seen that a necessary condition is that the RCFT fusion rules must exhibit an extra symmetry. We consider two particular perturbations of the Grassmannian superpotentials. The topological LG residues in one perturbation, introduced by Gepner, are shown to be a twisted version of the $SU(N)_k$ Verlinde dimensions. The residues in the other perturbation are the twisted Verlinde dimensions of another RCFT; these topological LG correlation functions are conjectured to be the correlation functions of the corresponding Grassmannian topological sigma model with a coupling in the action to instanton number.Comment: 16 page