  We introduce a new operad, which we call the Swiss-cheese operad. It mixes
naturally the little disks and the little intervals operads. The Swiss-cheese
operad is related to the configuration spaces of points on the upper half-plane
and points on the real line, considered by Kontsevich for the sake of
deformation quantization. This relation is similar to the relation between the
little disks operad and the configuration spaces of points on the plane. The
Swiss-cheese operad may also be regarded as a finite-dimensional model of the
moduli space of genus-zero Riemann surfaces appearing in the open-closed string
theory studied recently by Zwiebach. We describe algebras over the homology of
the Swiss-cheese operad.
