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Abstract

We construct a generalized class of quantum gravity condensate states, that
allows the description of continuum homogeneous quantum geometries within the
full theory. They are based on similar ideas already applied to extract
effective cosmological dynamics from the group field theory formalism, and thus
also from loop quantum gravity. However, they represent an improvement over the
simplest condensates used in the literature, in that they are defined by an
infinite superposition of graph-based states encoding in a precise way the
topology of the spatial manifold. The construction is based on the definition
of refinement operators on spin network states, written in a second quantized
language. The construction lends itself easily to be applied also to the case
of spherically symmetric quantum geometries.