Abstract Riemannian stratifications

Giacomo Monti Bragadin

Vol. 133 (1988), No. 1, 31–39

DOI: 10.2140/pjm.1988.133.31

Abstract

Let A be an abstract stratification. Assume that every stratum X is a riemannian manifold. We first give some conditions, under which it is possible to endow A with a suitable metric extending a well known technique of riemannian manifolds. Then stronger conditions are introduced in order that the metric space A becomes a G-space. An abstract stratification with all the above conditions is called an abstract riemannian stratification. Whitney stratifications are, in a natural way, riemannian.

Mathematical Subject Classification 2000

Primary: 58A35

Secondary: 53C70, 57N80

Milestones

Received: 24 January 1986

Revised: 6 July 1987

Published: 1 May 1988