Title: Equivariant homotopy theory for orbifolds

Dorette Pronk, Dalhousie University

(Joint Work with Laura Scull (UBC))

Abstract: Orbifolds and generalized (also called, good) maps form a
bicategory of fractions of Lie groupoids with respect to essential
equivalences (also called, Morita equivalences). I will discuss how
generalized maps between representable orbifolds can be represented
by pairs of equivariant maps: a span of an equivariant essential
equivalence and an arbitrary equivariant map. I will also give a
concrete description of the equivariant essential equivalences.

As a consequence of this we are able to start translating
equivariant homotopy invariants into new homotopy invariants for
orbifolds. I will describe several examples and discuss some of
the issues involved.