论文标题
重新审视了Yomdin-Gromov代数引理
The Yomdin-Gromov algebraic lemma revisited
论文作者
论文摘要
1987年，Yomdin证明了对Shub $ C^\ Infty $地图的SHUB熵猜想解决方案的一部分，这证明了对半ge式集合的平滑参数化的引理。该声明由Gromov进一步完善，该声明现在被称为Yomdin-Gromov代数引理。文献中出现了一些基于格罗莫夫草图的完整证明，但是由于某些技术问题，这些证据比格罗莫夫的原始演讲要复杂得多。 在本说明中，我们给出了遵循格罗莫夫的原始演示的证据。我们证明了一个更强的陈述，其中保证参数化图为\ emph {cellular}。事实证明，这种额外的限制，以及在O最低结构中可区分功能的一些基本引理，允许在没有技术困难的情况下进行诱导。
In 1987, Yomdin proved a lemma on smooth parametrizations of semialgebraic sets as part of his solution of Shub's entropy conjecture for $C^\infty$ maps. The statement was further refined by Gromov, producing what is now known as the Yomdin-Gromov algebraic lemma. Several complete proofs based on Gromov's sketch have appeared in the literature, but these have been considerably more complicated than Gromov's original presentation due to some technical issues. In this note we give a proof that closely follows Gromov's original presentation. We prove a somewhat stronger statement, where the parameterizing maps are guaranteed to be \emph{cellular}. It turns out that this additional restriction, along with some elementary lemmas on differentiable functions in o-minimal structures, allows the induction to be carried out without technical difficulties.
