Vol. 6, No. 4, 2013

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An orbit Cartan type decomposition of the inertia space of $\mathrm{SO}(2m)$ acting on $\mathbb R^{2m}$

Christopher Seaton and John Wells

Vol. 6 (2013), No. 4, 467–482
Abstract

We study the inertia space of 2m with the standard action of the special orthogonal group SO(2m). In particular, we indicate a decomposition of the inertia space that induces the orbit Cartan type stratification of the inertia space recently defined by C. Farsi, M. Pflaum, and the first author for an arbitrary smooth G-manifold where G is a compact Lie group.

Keywords
inertia space, stratification, special orthogonal group, Lie group
Mathematical Subject Classification 2010
Primary: 57S15, 58A35
Milestones
Received: 30 August 2012
Revised: 17 May 2013
Accepted: 19 May 2013
Published: 8 October 2013

Communicated by Michael Dorff
Authors
Christopher Seaton
Department of Mathematics and Computer Science
Rhodes College
2000 North Parkway
Memphis, TN 38112
United States
John Wells
Department of Mathematics
University of Hawaii at Manoa
2565 McCarthy Mall
Honolulu, HI 96822
United States