The Chern-Simons character of a lattice gauge field<p>
by Anthony V. Phillips and David A. Stone<p><p>
Abstract<p>

Let U be a generic SU(2)-valued latticegauge field on a triangulation
of a manifold X of dimension at least 3. An algorithm is given for constructing from
U a principal SU(2)-bundle over X, and in that bundle a connection with the 
following property. Its Chern-Simons character can be computed as the sum of
local contributions (one for each 3-simplex of the triangulation), each one
the sum of a one-dimensional integral and five other terms which are 
volumes of elementary regions in the 3-sphere. For any 3-cycle this sum,
reduced mod Z, is gauge invariant. This character is related in the appropriate way
to real and integral 4-cocyles representing the second Chern class of
the bundle. If U has sufficiently small plaquette products, the isomorphism
class of the bundle is shown to depend only on U, and not on 
details of the construction.<p>

 in Louis Kauffman and Randy Baadhio, <i>eds.</i>,
         Quantum Topology, World Scientific 1993, 244-291