Stratifications of Inertia Spaces of Compact Lie Group Actions

Journal of Singularities
volume 13 (2015), 107-140

Received 24 October 2013. Received in revised form 8 April 2014.

DOI: 10.5427/jsing.2015.13f

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Abstract:

We study the topology of the inertia space of a smooth G-manifold M where G is a compact Lie group. We construct an explicit Whitney stratification of the inertia space, demonstrating that the inertia space is a triangulable differentiable stratified space. In addition, we demonstrate a de Rham theorem for differential forms defined on the inertia space with respect to this stratification.

Keywords:

Lie group, G-manifold, stratified space, differentiable space, inertia space

Mathematical Subject Classification:

57S15, 58A35; Secondary 22C05, 32S60, 57R18