  For a fixed closed manifold $P$, we construct a cobordism category of
embedded manifolds with a single Baas-Sullivan singularity of type $P$. Our
main theorem identifies the homotopy type of the classifying space of this
cobordism category with that of the infinite loop-space of a certain spectrum
related to the spectrum $\text{MT}(d)$ introduced in [arXiv:math/0605249]. We
obtain an analogue of the Bockstein-Sullivan exact couple that arises between
the classical bordism theories $MO$ and $MO_{P}$ on the level of cobordism
categories.

Algebraic Topology;Differential Geometry;Geometric Topology