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|Paper IPM / Physic / 6527||
The lattice definition of the two-dimensional topological quantum field theory
[Fukuma et al., Commun. Math. Phys. 161, 157 (1994)] is
generalized to arbitrary (not necessarily orientable) compact surfaces. It is
shown that there is a one-to-one correspondence between real associative
and the topological state sum invariants defined on such surfaces.
The partition and n-point functions on all two-dimensional surfaces
(connected sums of the Klein bottle or projective plane and
g-tori) are defined and computed for arbitary *-algebras
in general, and for the
group ring A=\BbbR[G] of discrete groups G, in particular.
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