  The dynamics of networks of neuronal cultures has been recently shown to be
strongly dependent on the network geometry and in particular on their
dimensionality. However, this phenomenon has been so far mostly unexplored from
the theoretical point of view. Here we reveal the rich interplay between
network geometry and synchronization of coupled oscillators in the context of a
simplicial complex model of manifolds called Complex Network Manifold. The
networks generated by this model combine small world properties (infinite
Hausdorff dimension) and a high modular structure with finite and tunable
spectral dimension. We show that the networks display frustrated
synchronization for a wide range of the coupling strength of the oscillators,
and that the synchronization properties are directly affected by the spectral
dimension of the network.
