Sewing Yang-Mills measures and moduli spaces over compact surfaces

Consider a closed surface Sigma obtained by pasting two surfaces Sigma(1) and Sigma(2) along some of their boundary components. A formula is derived expressing quantum Yang-Mills functional integrals for Sigma in terms of the corresponding integrals for the surfaces Sigma(i). Using this, a formula is derived which expresses the symplectic volume measure on the moduli space of nat SU(2) connections over a closed Riemann surface Sigma in terms of the corresponding volume measures for the surfaces Sigma(1) and Sigma(2),when the latter have one boundary component each. (C) 1998 Academic Press.