Embedding calculus and smooth structures

Knudsen, Ben¹ ; Kupers, Alexander²

¹ Department of Mathematics, Northeastern University, Boston, MA, United States
² Department of Mathematics, University of Toronto, Toronto, ON, Canada

Geometry & topology, Tome 28 (2024) no. 1, pp. 353-392.

Résumé

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.

Détail

DOI : 10.2140/gt.2024.28.353

Keywords: embedding calculus, smooth structures, $4$–manifolds

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