2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152198We prove the Chern-Weil formula for SU(n+1)-singular connections over the complement of an embedded oriented surface in smooth four manifolds. The expression of the representation of a number as a sum of nonvanishing squares is given in terms of the representations of a number as a sum of squares. Using the number theory result, we study the irreducible SU(n+1)-representations of the fundamental group of the complement of an embedded oriented surface in smooth four manifolds.Latex, 14 pagesDifferential Geometry58D27, 57R57, 11D85, 11E25text