Geodesic
Classifying tangent structures using Weil algebras
Theory and applications of categories, Tome 32 (2017), pp. 286-337.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

At the heart of differential geometry is the construction of the tangent bundle of a manifold. There are various abstractions of this construction, and of particular interest here is that of Tangent Structures. Tangent Structure is defined via giving an underlying category M and a tangent functor T along with a list of natural transformations satisfying a set of axioms, then detailing the behaviour of T in the category End(M). However, this axiomatic definition at first seems somewhat disjoint from other approaches in differential geometry. The aim of this paper is to present a perspective that addresses this issue. More specifically, this paper highlights a very explicit relationship between the axiomatic definition of Tangent Structure and the Weil algebras (which have a well established place in differential geometry).
Publié le :
Classification : 18D99, 53A99
Keywords: Tangent Structure, Weil algebra 
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     author = {Poon Leung},
     title = {Classifying tangent structures using {Weil} algebras},
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     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a8/}
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Poon Leung. Classifying tangent structures using Weil algebras. Theory and applications of categories, Tome 32 (2017), pp. 286-337. http://geodesic.mathdoc.fr/item/TAC_2017_32_a8/