Whitney分层是锥形光滑的
Whitney stratifications are conically smooth
AI总结：
本文证明了任何Whitney分层空间都允许标准的锥形光滑结构，从而在锥形光滑空间理论与微分拓扑的经典分层空间示例之间建立了联系。
摘要：
Ayala、Francis和Tanaka引入了分层空间上的锥形光滑结构概念。这是分层拓扑空间背景下微分结构的良好类似物，满足奇点消解和柄体分解等良好性质。本文证明了Ayala、Francis和Tanaka的猜想：任何Whitney分层空间都允许标准的锥形光滑结构。从而在锥形光滑空间理论与微分拓扑的经典分层空间示例之间建立了联系。
英文摘要：
The notion of conically smooth structure on a stratified space was introduced by Ayala, Francis and Tanaka. This is a very well behaved analogue of a differential structure in the context of stratified topological spaces, satisfying good properties such as the existence of resolutions of singularities and handlebody decompositions. In this paper we prove Ayala, Francis and Tanaka's conjecture that any Whitney stratified space admits a canonical conically smooth structure. We thus establish a connection between the theory of conically smooth spaces and the classical examples of stratified spaces from differential topology.
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