Observers, local measurements, and topology

An observer which propagates in a spacetime with dynamical gravity has access to an algebra of observables which is expected to be a von Neumann algebra with a trace. The observer can use projections from the algebra to perform local measurements. By using this fact we construct a simplicial complex out of measurements recorded on the worldline of the observer and we propose that such a complex captures topological information about spacetime, even when this is fluctuating.