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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)

Information

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

[1]Bertram, W., ‘Differential geometry over general base fields and rings’, Mem. Amer. Math. Soc. 192(900) (2008).Google Scholar
[2]Kapranov, M., ‘Free Lie algebroids and the space of paths’, Selecta Math. 13 (2007), 277–319.CrossRefGoogle Scholar
[3]Kock, A. and Lavendhomme, R., ‘Strong infinitesimal linearity, with applications to strong difference and affine connections’, Cah. Topol. Géom. Différ. 25 (1984), 311–324.Google Scholar
[4]Mackenzie, K. C. H., General Theory of Lie Groupoids and Lie Algebroids, London Mathematical Society Lecture Note Series, 213 (Cambridge University Press, Cambridge, 2005).CrossRefGoogle Scholar
[5]Moerdijk, I. and Reyes, G. E., Models for Smooth Infinitesimal Analysis (Springer, Berlin, 1991).CrossRefGoogle Scholar
[6]White, J. E., The Method of Iterated Tangents with Applications in Local Riemannian Geometry, Monographs and Studies in Mathematics, 13 (Pitman, Boston, 1982).Google Scholar