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Spin geometry and Dirac operators have found manifold applications in both physics and mathematics. One of the main objects of study in this area is the spinor bundle over a (finite-dimensional) manifold. Motivated by questions in string theory we will take some first steps in defining a spinor bundle over the loop space of a manifold. We shall equip this bundle with extra structure, namely that of "fusion over overlapping loops" which will be defined in the talk. Our construction uses tools from the theories of loop spaces, of infinite dimensional Clifford algebras, and of bimodules of von Neumann algebras.

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