A ug 2 00 0 Local subgroupoids II : Examples and properties ∗

Local Subgroupoids Ii: Examples and Properties *

The notion of local subgroupoid as a generalisation of a local equivalence relation was defined in a previous paper by the first two authors. Here we the notion of star path connectivity for a Lie groupoid to give an important new class of examples, generalising the local equivalence relation of a foliation, and develop in this new context basic properties of coherence, due earlier to Rosenthal...

Some Results for the Local Subgroupoids

The notion of local subgroupoids as generalition of a local equivalence relations was defined by the first author and R.Brown. Here we investigate some relations between transitive components and coherence properties of the local subgroupoids.

Lie Local Subgroupoids and Their Monodromy

The notion of local equivalence relation on a topological space is generalised to that of local subgroupoid. Properties of coherence are considered. The main result is notions of holonomy and monodromy groupoid for certain Lie local subgroupoids.

ar X iv : g r - qc / 0 31 00 91 v 2 1 4 A ug 2 00 6 Semilinear wave equations on the Schwarzschild manifold I : Local Decay Estimates

The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type inequalities.

ar X iv : 0 70 8 . 26 18 v 1 [ as tr o - ph ] 2 0 A ug 2 00 7 Using Local Volume data to constrain Dark Matter dynamics