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A geometric proof of the existence of Whitney stratifications

Vadim Kaloshin
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Abstract

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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Vadim Kaloshin. 2000-10-13. A geometric proof of the existence of Whitney stratifications. https://arxiv.org/abs/math/0010144

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