LINEARIZATION OF REGULAR PROPER GROUPOIDS

Abstract

Let is proper. We show that, if is an orbit of finite type (i.e. which admits a proper function with finitely many critical points), then the restriction is isomorphic to a similar restriction of the action groupoid for the linear action of the transitive groupoid on the normal bundle . The proof uses a deformation argument based on a cohomology vanishing theorem, along with a slice theorem which is derived from a new result on submersions with a fibre of finite type.AMS 2000 Mathematics subject classification: Primary 58H05. Secondary 57R99