A geometric proof of the existence of Whitney stratifications

Details A geometric proof of the existence of Whitney stratifications A geometric proof of the existence of Whitney stratifications

2000-10-13

arxiv.org/abs/math/0010144v1

Mathematics

Algebraic Geometry

7 pages

Scientific paper

A stratification of a singular set, e.g. an algebraic or analytic variety, is, roughly, a partition of it into manifolds so that these manifolds fit together "regularly". A classical theorem of Whitney says that any complex analytic set has a stratification. This result was extended by Lojasiewicz to real (semi)analytic sets. In this paper we present a short geometric proof of existence of stratifications based on Thom's transversality theorem and Milnor's curve selection lemma and not relying on difficult results of Lojasiewicz.

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