Speaker: Christopher Seaton (Rhodes College)
2012.09.20 |
Date | Wed 12 Sep |
Time | 16:00 — 17:00 |
Location | Aud. D3 (1531-215) |
Abstract:
Let be a compact Lie group and let
be a smooth
-manifold. If
happens to act locally freely on
, then the quotient of
by the
-action is an example of an orbifold. In the study of the geometry of orbifolds, an object called the inertia orbifold has played a major role. The inertia orbifold is a disjoint union of orbifolds given by the quotient of the space of loops of the translation groupoid, a smooth manifold, by a natural action of the translation groupoid itself.
If the action of is not assumed to be locally free, then the space of loops of the translation groupoid is no longer a smooth manifold and the quotient is no longer an orbifold. In this case, we refer to the quotient of the space of loops as the inertia space of the
-manifold
. We will describe an explicit Whitney stratification of the inertia space. Using this stratification, we will present a de Rham theorem for cohomology of differential forms on the inertia space with respect to this stratification. (Joint work with Carla Farsi and Markus Pflaum)