Abstract
We prove the Chern-Weil formula for SU( n + l)-singular connections over the complement of an embedded oriented surface in a smooth four-manifold. The number of representations of a positive integer n as a sum of nonvanishing squares is given in terms of the number of its representations as a sum of squares. Using this number-theoretic result, we study the irreducible SU( n +1)-representations of the fundamental group of the complement of an embedded oriented surface in smooth four-manifold.
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