Mathematics – Differential Geometry
Scientific paper
2011-12-20
Mathematics
Differential Geometry
64 pages, 5 figures
Scientific paper
One way to geometrically encode the singularities of a stratified pseudomanifold is to endow its interior with an iterated fibred cusp metric. For such a metric, we develop and study a pseudodifferential calculus generalizing the \Phi-calculus of Mazzeo and Melrose. Our starting point is the observation, going back to Melrose, that a stratified pseudomanifold can be `resolved' into a manifold with fibred corners. This allows us to define pseudodifferential operators as conormal distributions on a suitably blown-up double space. Various symbol maps are introduced, leading to the notion of full ellipticity. This is used to construct refined parametrices and to provide criteria for the mapping properties of operators such as Fredholmness or compactness. We also introduce a semiclassical version of the calculus and use it to establish a Poincar\'e duality between the K-homology of the stratified pseudomanifold and the K-group of fully elliptic operators.
Debord Claire
Lescure Jean-Marie
Rochon Frederic
No associations
LandOfFree
Pseudodifferential operators on manifolds with fibred corners does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Pseudodifferential operators on manifolds with fibred corners, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pseudodifferential operators on manifolds with fibred corners will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-54651