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  • Title
    Blow-up constructions for Lie groupoids and a Boutet de Monvel type calculus
  • Author
    Debord, Claire ; Skandalis, Georges
  • Is part of
    Münster Journal of Mathematics, Issue Münster Journal of Mathematics, page 1-40
  • Published
    2021
  • Language
    English
  • Document type
    Journal Article
  • URN
    urn:nbn:de:hbz:6-59019640923 
  • DOI
    10.17879/59019640550 
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Abstract
  • 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.
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