2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148388We prove formulas (found by Witten in 1992 using physical methods) for intersection pairings in the cohomology of the moduli space M(n,d) of stable holomorphic vector bundles of rank n and degree d (assumed coprime) on a Riemann surface of genus g greater than or equal to 2. We also use these formulas for intersection numbers to obtain a proof of the Verlinde formula for the dimension of the space of holomorphic sections of a line bundle over M(n,d).77 pages, LaTeX version 2.09. This is the text of the revised version which will appear in Annals of Mathematics. An error in Section 2 of the previous version has been correctedAlgebraic GeometryDifferential GeometryHigh Energy Physics - Theorytext