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Structure of Topological Lattice Field Theories in Three Dimensions
We construct and classify topological lattice field theories in three
dimensions. After defining a general class of local lattice field theories, we
impose invariance under arbitrary topology-preserving deformations of the
underlying lattice, which are generated by two new local lattice moves.
Invariant solutions are in one--to--one correspondence with Hopf algebras
satisfying a certain constraint. As an example, we study in detail the
topological lattice field theory corresponding to the Hopf algebra based on the
group ring \C[G], and show that it is equivalent to lattice gauge theory at
zero coupling, and to the Ponzano--Regge theory for SU(2).Comment: 63 pages, 46 figure
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