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Longitudinal b-operators, Blups and Index theorems. (arXiv:1711.11197v1 [math.KT])
来源于:arXiv
Using recently introduced Debord-Skandalis Blup's groupoids we study index
theory for a compact foliated manifold with boundary inducing a foliation in
its boundary. For this we consider first a blup groupoid whose Lie algebroid
has sections consisting of vector fields tangent to the leaves in the interior
and tangent to the leaves of the foliation in the boundary. In particular the
holonomy $b$-groupoid allows us to consider the appropriate pseudodifferential
calculus and the appropriate index problems.
In this paper we further use the blup groupoids, and in particular its
functoriality properties, to actually get index theorems. For the previous
geometric situtation we have two index morphisms, one related to ellipticity
and a second one related to fully ellipticity (generalized Fredholmness). For
the first we are able to extend the longitudinal Connes-Skandalis index theorem
and use it to get that every $b$-longitudinal elliptic operator can be
perturbed (up to stable homotopy) with 查看全文>>