  The usual epistemic S5 model for multi-agent systems is a Kripke graph, whose
edges are labeled with the agents that do not distinguish between two states.
We propose to uncover the higher dimensional information implicit in the Kripke
graph, by using as a model its dual, a chromatic simplicial complex. For each
state of the Kripke model there is a facet in the complex, with one vertex per
agent. If an edge (u,v) is labeled with a set of agents S, the facets
corresponding to u and v intersect in a simplex consisting of one vertex for
each agent of S. Then we use dynamic epistemic logic to study how the
simplicial complex epistemic model changes after the agents communicate with
each other. We show that there are topological invariants preserved from the
initial epistemic complex to the epistemic complex after an action model is
applied, that depend on how reliable the communication is. In turn these
topological properties determine the knowledge that the agents may gain after
the communication happens.
