论文标题
嵌入微积分和平滑结构
Embedding calculus and smooth structures
论文作者
论文摘要
我们研究了嵌入泰勒塔对源和目标平滑结构的依赖性。我们证明，嵌入演算并不能区分尺寸4中的外来平滑结构，这意味着对维罗的问题有负答案。相比之下，我们表明嵌入积分确实在较高维度中区分了某些外来球体。作为独立感兴趣的技术工具，我们证明了嵌入微积分塔极限的同位素扩展定理，我们用它来研究其他几个示例。
We study the dependence of the embedding calculus Taylor tower on the smooth structures of the source and target. We prove that embedding calculus does not distinguish exotic smooth structures in dimension 4, implying a negative answer to a question of Viro. In contrast, we show that embedding calculus does distinguish certain exotic spheres in higher dimensions. As a technical tool of independent interest, we prove an isotopy extension theorem for the limit of the embedding calculus tower, which we use to investigate several further examples.
