A geometric proof of the existence of Whitney stratifications

Vadim Kaloshin (American Institute of Mathematics)

A geometric proof of the existence of Whitney stratifications

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arxiv math/0010144 v1 pith:FNIIWYVH submitted 2000-10-13 math.AG

Vadim Kaloshin (American Institute of Mathematics) This is my paper · ORCID

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keywords analyticexistencegeometriclojasiewiczmanifoldsproofstratificationstratifications

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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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