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WHAT IS THE HIGHER-DIMENSIONAL INFINITESIMAL GROUPOID OF A MANIFOLD?

Part of: Topological and differentiable algebraic systems

Published online by Cambridge University Press:  14 June 2011

DENNIS BORISOV
DENNIS BORISOV*
Affiliation:
Max Planck Institute for Mathematics, PO Box 7280, 53072 Bonn, Germany (email: dennis.borisov@gmail.com)
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Abstract

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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 nonlinear cohomology.

Keywords

Lie algebroidLie–Rinehart algebrashigher categoriespolyvector fields

MSC classification

Secondary: 22A22: Topological groupoids (including differentiable and Lie groupoids)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 90 , Issue 2 , April 2011 , pp. 155 - 170
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

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