  A key challenge for many quantum gravity approaches is to construct states
that describe smooth geometries on large scales. Here we define a family of
$(2+1)$-dimensional quantum gravity states which arise from curvature
excitations concentrated at point like defects and describe homogeneously
curved geometries on large scales. These states represent therefore vacua for
three-dimensional gravity with different values of the cosmological constant.
They can be described by an anomaly-free first class constraint algebra
quantized on one and the same Hilbert space for different values of the
cosmological constant. A similar construction is possible in four dimensions,
in this case the curvature is concentrated along string-like defects and the
states are vacua of the Crane-Yetter model. We will sketch applications for
quantum cosmology and condensed matter.
