Embedding calculus and smooth structures
arXiv:2006.03109 · doi:10.2140/gt.2024.28.353
Abstract
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.
arXiv comment35 pages, 1 figure. Final version
References in corpus (9)
- Embeddings from the point of view of immersion theory: Part I
- Embeddings from the point of view of immersion theory: Part II
- Spaces of smooth embeddings and configuration categories
- Multiple disjunction for spaces of smooth embeddings
- Context-free manifold calculus and the Fulton-MacPherson Operad
- Some finiteness results for groups of automorphisms of manifolds
- The cohomology of Torelli groups is algebraic
- Dalian notes on rational Pontryagin classes
- Spaces of knotted circles and exotic smooth structures