Title of Paper: On the homotopy type of Lie groupoids

Author: Hellen Colman

AMS Classification numbers: 22A22; 18D05; 55P15

math.AT/0612257

Address of Author: Department of Mathematics, Wilbur Wright College,
4300 N. Narragansett Avenue, Chicago, IL 60634 USA 

Email address of Author: hcolman@ccc.edu

Text of Abstract:
We propose a notion of groupoid homotopy for generalized maps. This
notion of groupoid homotopy generalizes the notions of natural
transformation and strict homotopy for functors. The groupoid homotopy
type of a Lie groupoid is shown to be invariant under Morita
equivalence. As an application we consider orbifolds as groupoids and
study the orbifold homotopy between orbifold maps induced by the
groupoid homotopy.