In this talk, after recalling basic facts on groupoids, we will see that the structure of a groupoid G is entirely determined by giving invariant subsets by cyclic permutations of the Cartesian product G^k for k=0,…,3 and satisfying some additional properties. We will then focus our attention on a special type of groupoids, namely VB-groupoids and see how this point of view allows to find very simply the construction of the dual groupoid of a VB-groupoid. In particular, we recover the famous Weinstein’s cotangent groupoid. Finally, we will construct a Fourier transform in this situation which induces an isomorphism between the C*-algebra of a VB-groupoid E and the C*-algebra of the VB-groupoid dual E*.This is a work in progress with Georges Skandalis.

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