Defines the fibered cusp b-pseudodifferential operator calculus Ψ^*_{Φ,b}(X) on manifolds with corners, proves a relative index theorem, and applies it to index theorems for non-closed Z/k-manifolds.
Blowup constructions for Lie groupoids and a Boutet de Monvel type calculus
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abstract
We present natural and general ways of building Lie groupoids, by using the classical procedures of blowups and of deformations to the normal cone. Our constructions are seen to recover many known ones involved in index theory. The deformation and blowup groupoids obtained give rise to several extensions of $C^*$-algebras and to full index problems. We compute the corresponding K-theory maps. Finally, the blowup of a manifold sitting in a transverse way in the space of objects of a Lie groupoid leads to a calculus, quite similar to the Boutet de Monvel calculus for manifolds with boundary.
years
2019 2verdicts
UNVERDICTED 2representative citing papers
Review summarizing Lie groupoids in noncommutative geometry, covering fundamentals, advances in index theory, and open questions.
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Fibered Cusp b-Pseudodifferential Operators and its Applications
Defines the fibered cusp b-pseudodifferential operator calculus Ψ^*_{Φ,b}(X) on manifolds with corners, proves a relative index theorem, and applies it to index theorems for non-closed Z/k-manifolds.
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Lie groupoids, pseudodifferential calculus and index theory
Review summarizing Lie groupoids in noncommutative geometry, covering fundamentals, advances in index theory, and open questions.