Fixed, thanks for the heads up

]]>You may enjoy Maurice Herlihy’s exploration of the light combinatorial topology has to shed on distributed algorithms in *Distributed Computing through Combinatorial Topology*.

As I understand it, one can model the state of a distributed computation as a simplicial complex (a higher-dimensional generalization of a graph). The steps in a communications protocol can then be modeled as a continuous transformation of that simplicial complex (i.e., mapping one complex to another).

Many classic problems in distributed computing then become: can one simplicial complex representing the start state of the problem be continuously transformed into another representing the desired end-state of the problem? In many cases (e.g. a connected complex transformed into a disconnected one, or a complex with one “hole” transformed into a complex with a different number of “holes”), the answer is a pretty trivial (from the point of view of a topologist) “no”.

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