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- W2171469897 abstract "We present some plausible denitions for the tangent grupoid of a manifold M, as well as some of the known applications of the structure. This is a kind of introductory note. Students rst meet the grupoid law when they learn about ane vectors, this is, ordered pairs of points jointly with an addition rule: ~ xy + ~ yz = ~ xz. Sometimes they are able even to notice the ambiguity of any attempt to add a multiplication by scalars, before being driven to quotient by an equivalence relationship, thand then to arrive to the standard concept of free vector. Perhaps the simplest mathematical object preserving the naive vector law is the tangent grupoid. It is basically the union of two old pieces of dieren tial geometry: a well known one, the tangent bundle, living in the envolvent of the manifold, and an older but less controlled one, nite dierences, which can be thought to live in the secant envolvent of the manifold. A giant step into the analysis of this structure was given by A. Connes, namely to study the algebra of functions over the grupoid, using the tools of non commutative geometry [3]. We aim here to present this object in a form more close to standard geometry books (e.g.[2, 6]), so it becomes easier to focus the geometric signicance of its use." @default.
- W2171469897 created "2016-06-24" @default.
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- W2171469897 date "1997-10-23" @default.
- W2171469897 modified "2023-10-01" @default.
- W2171469897 title "Introduction to the Tangent Grupoid" @default.
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- W2171469897 hasPublicationYear "1997" @default.
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