Stratifications of Inertia Spaces of Compact Lie Group Actions

Carla Farsi, Markus J. Pflaum, Christopher Seaton

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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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.


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

Mathematical Subject Classification:

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

Author(s) information:

Carla Farsi Markus J. Pflaum Christopher Seaton
Department of Mathematics Department of Mathematics Dept. of Mathematics & Computer Science
University of Colorado at Boulder University of Colorado at Boulder Rhodes College
Campus Box 395 Campus Box 395 2000 N. Parkway
Boulder, CO 80309-0395 Boulder, CO 80309-0395 Memphis, TN 38112
email: email: pflaum@Colorado.EDU email: