Physics

8 downloads 50961 Views 3MB Size Report
Brooklyn College, City University of New York, Brooklyn, NY 11210, USA. Abstract. .... o of its vertices in which the vertices of each simplex are totally ordered.

Communications in Commun. Math. Phys. 131, 255-282 (1990)

Mathematical

Physics

© Springer-Verlag 1990

The Computation of Characteristic Classes of Lattice Gauge Fields Anthony V. Phillips1* and David A. Stone2** 1 2

State University of New York at Stony Brook, Stony Brook, NY 11784, USA Brooklyn College, City University of New York, Brooklyn, NY 11210, USA

Abstract. A GL(p, C)-valued lattice gauge field u on a simplicial complex determines a principal GL(p, C)-bundle ξ if the plaquette products are sufficiently small with respect to the maximum distortion coefficient of the transporters. A representative cocycle cq for the qth Chern class of ξ can be computed on each 2g-simplex σ by taking cq(σ) to be the intersection number of a certain singular 2