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). Usi ng this, a formula is derived which expresses the symplectic volume me asure on the moduli space of nat SU(2) connections over a closed Riema nn surface Sigma in terms of the corresponding volume measures for the surfaces Sigma(1) and Sigma(2),when the latter have one boundary comp onent each. (C) 1998 Academic Press.