What is the higher dimensional infinitesimal groupoid of a manifold?

Mathematics – Quantum Algebra

Scientific paper

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Scientific paper

The construction (by Kapranov) of the space of infinitesimal paths on a
manifold is extended to include higher dimensional infinitesimal objects,
encoding contractions of infinitesimal loops. This full infinitesimal groupoid
is shown to have the algebra of polyvector fields as its non-linear cohomology.

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