# Seminar: A stratification of the inertia space of a G-manifold for compact Lie group G

Speaker: Christopher Seaton (Rhodes College)

2012.09.20 | Christine Dilling

 Date Wed 12 Sep Time 16:00 — 17:00 Location Aud. D3 (1531-215)

Abstract:

Let $~G$ be a compact Lie group and let $~M$ be a smooth $~G$-manifold. If $~G$ happens to act locally freely on $~M$, then the quotient of $~M$ by the $~G$-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 $~G$ 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 $~G$-manifold $~M$. 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)

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