Mathematical Sciences: "Geometry of Charateristic Classes"

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9504237 McLaughlin The proposed research lies in the interface of differential topology and mathematical physics. More specifically, it deals with the so called Wess-Zumino-Witten vector bundle on Teichmuller space and is an attempt to give a rigorous formula for the projectively flat connection on this bundle. In recent years several unexpected relations between topology and mathematical physics have been discovered. If completely successful, the proposed research - which is originally motivated by problems in quantum field theory - will likely shed a new light on the study of 3-dimensional spaces and knot theory.