Abstract
The relation between standard loop quantum cosmology (LQC) and full loop quantum gravity (LQG) fails already at the first nontrivial step: the configuration space of LQC cannot be embedded into the configuration space of full LQG due to a topological obstruction. We investigate this obstruction in detail, because many topological obstructions are the source of physical effects. For this, we derive the topology of a large class of subspaces of the LQG configuration space. This allows us to find the extension of the standard LQC configuration space that admits an embedding in agreement with Fleischhack (arXiv:1010.0449v1 [math-ph]). We then construct the embedding for flat FRW LQC and find the reassuring result that it coincides asymptotically with standard LQC.
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