Blow-up constructions for Lie groupoids and a Boutet de Monvel type calculus
We present natural and general ways of building Lie groupoids, by using the classical procedures of blow-ups and of deformations to the normal cone. Our constructions are seen to recover many known ones involved in index theory. The deformation and blow-up groupoids obtained give rise to several ext...
Verfasser: | |
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Dokumenttypen: | Artikel |
Medientypen: | Text |
Erscheinungsdatum: | 2021 |
Publikation in MIAMI: | 16.02.2021 |
Datum der letzten Änderung: | 16.02.2021 |
Quelle: | Münster Journal of Mathematics, 14 (2021), S. 1-40 |
Verlag/Hrsg.: |
Mathematisches Institut (Universität Münster)
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Angaben zur Ausgabe: | [Electronic ed.] |
Fachgebiet (DDC): | 510: Mathematik |
Lizenz: | InC 1.0 |
Sprache: | Englisch |
Format: | PDF-Dokument |
URN: | urn:nbn:de:hbz:6-59019640923 |
Weitere Identifikatoren: | DOI: 10.17879/59019640550 |
Permalink: | https://nbn-resolving.de/urn:nbn:de:hbz:6-59019640923 |
Onlinezugriff: | mjm_2021_14_1-40.pdf |
We present natural and general ways of building Lie groupoids, by using the classical procedures of blow-ups and of deformations to the normal cone. Our constructions are seen to recover many known ones involved in index theory. The deformation and blow-up groupoids obtained give rise to several extensions of C*-algebras and to full index problems. We compute the corresponding K-theory maps. Finally, as an application, we use the blow-up of a manifold sitting in a transverse way in the space of objects of a Lie groupoid to construct a calculus which is quite similar to the Boutet de Monvel calculus for manifolds with boundary.