  We solve a conjecture of Morgan and Szabo (Embedded genus 2 surfaces in
four-manifolds, Preprint) about the relationship of the basic classes of two
four-manifolds $X_i$ of simple type with $b_1=0$, $b^+>1$, such that there are
embedded Riemann surfaces of genus $g \geq 2$ and self-intersection zero (and
representing odd homology classes) with the basic classes of the manifold X
which appears as a connected sum along the surfaces (supposing this latter one
is of simple type). This is also expressed as constraints in the basic classes
of X. The result is in accordance with the results on Seiberg-Witten invariants
(Morgan, Szabo and Taubes, A product formula for the Seiberg-Witten invariants
and the generalized Thom conjecture).
