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 use 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 in the special case. These results are required for further applications to holonomy and monodromy.
arXiv Mathematics e-prints
- Pub Date:
- August 2000
- Mathematics - Differential Geometry;
- Mathematics - Category Theory;
- 18 pages. replacement gives a change to the use of the flat condition for a path connection, and adds a reference on locally Lie groupoids