Dynamical Pure Quantum Simplicial Complexes

Pure simplicial complexes play a fundamental role in algebraic topology and stochastic topology. In this talk we discuss quantum analogues of pure simplicial complexes which can play an important role in Background Independent formulations of quantum gravity. We use generalized symmetrization and anti-symmetrization procedures to formulate unlabeled quantum simplicial complexes where the vertices are treated as indistinguishable. Then we examine a dynamical toy models of interacting quantum simplicial complexes in which the low energy states have geometric properties, serving as building blocks for emergent geometry from pre-geometric quantum states.