#### 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 ${ℝ}^{2m}$ with the standard action of the special orthogonal group $SO\left(2m\right)$. 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
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