Local subgroupoids II: Examples and properties
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- August 2000
- DOI:
- 10.48550/arXiv.math/0008165
- arXiv:
- arXiv:math/0008165
- Bibcode:
- 2000math......8165B
- Keywords:
-
- Mathematics - Differential Geometry;
- Mathematics - Category Theory;
- 18F20;
- 18F05;
- 22E99;
- 22A22;
- 58H05
- E-Print:
- 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