A comparison of the Georgescu and Vasy spaces associated to the N-body problems
by
Bernd Ammann, Jérémy Mougel, Victor Nistor


A comparison of the Georgescu and Vasy spaces associated to the N-body problems (.pdf)

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Abstract

We show that the space introduced by Vasy in order to construct a pseudodifferential calculus adapted to the N-body problem can be obtained as the primitive ideal spectrum of one of the N-body algebras considered by Georgescu. In the process, we provide an alternative description of the iterated blow-up space of a manifold with corners with respect to a clean semilattice of adapted submanifolds (i.e. p-submanifolds). Since our constructions and proofs rely heavily on manifolds with corners and their submanifolds, we found it necessary to clarify the various notions of submanifolds of a manifold with corners.
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The Paper was written on 21.10.2019
Last update 21.10.2019