On the bisections of a local Lie grpoupod

Abstract

In this paper, we study the local Lie group structure associated with the space of admissible bisections of a local Lie groupoid over a compact manifold. We further investigate the relation of this local Lie group to the Lie algebra of sections of the associated Lie algebroid. In addition, we prove that the globalizability of a local Lie groupoid implies the globalizability of its associated local Lie group of bisections