Applied Topology

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The main objective of this research project is to drive forward the subject of Applied Topology on several fronts, providing a major advancement as a total result. We propose to work in 2 main directions: combinatorial torsions and evasiveness, and topology in concurrency.In the first direction, we plan to strengthen the theoretical foundations of combinatorial alge- braic topology by using a novel strategy to approach a major conjecture in the field.In the second direction, we want to bring together the existing developments on concurrency and theoretical distributed computing and thus develop what we call the topology of knowl- edge. Also here there is a number of explicit conjectures which we plan to attack.The whole project is suffused with ideas of quantitative topology, where the actual simplicial subdivision gains special importance.