, Volume 30, Issue 4, pp 425-445

Triangulation of stratified fibre bundles

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Abstract

We prove that for any stratified fibre bundle p:A·M (A being the underlying space of an abstract prestratification and M a smooth manifold) and any triangulation of M there exists a triangulation of A such that p becomes linear with respect to these triangulations. In particular, any abstract prestratification is triangulable. As a corollary we obtain that the orbit space of a smooth action of a compact Lie group is triangulable.

This paper was written while the author was a visiting professor at the Institute of Mathematics of the University of Genova.