TY  - JOUR
AB  - 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.
AU  - Debord, Claire
AU  - Skandalis, Georges
DA  - 2021
DO  - 10.17879/59019640550
LA  - eng
IS  - Münster Journal of Mathematics
M2  - 1
PY  - 2021
SP  - 1-40
T2  - Münster Journal of Mathematics
TI  - Blow-up constructions for Lie groupoids and a Boutet de Monvel type calculus
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:6-59019640923
Y2  - 2024-11-22T12:10:00
ER  -