Analysis of geometric operators on open manifolds: A groupoid approach

摘要

We use algebras of pseudodifferential operators on groupoids to studygeometric operators on non-compact manifolds and singular spaces. The firststep is to establish that the geometric operators are in our algebras. Thisthen leads to criteria for Fredholmness for geometric operators on suitablenon-compact manifolds, as well as to an inductive procedure to study theiressential spectrum. As an application, we answer a question of Melrose on theessential spectrum of the Laplace operator on manifolds with multi-cylindricalends.