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- W3164644443 abstract "Given a knot $s:S^{k-1}hookrightarrowpartial M$ with a framed dual sphere $G:S^{d-k}hookrightarrowpartial M$, we describe the homotopy type of the space of neat embeddings $D^khookrightarrow M^d$, with boundary $s$, as the loop space of neatly embedded $(k-1)$-disks in the manifold obtained from $M$ by attaching a handle to $G$. As a consequence, we conclude that the Dax invariant gives a complete isotopy classification of such disks in a 4-manifold. Moreover, we compute the resulting group structure on the set of these isotopy classes and show that it is nonabelian in most cases. Finally, we recover all previous results for spheres and prove that for them the Dax invariant reduces to the Freedman--Quinn invariant." @default.
- W3164644443 created "2021-06-07" @default.
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- W3164644443 date "2021-05-27" @default.
- W3164644443 modified "2023-09-27" @default.
- W3164644443 title "A space level light bulb theorem for disks." @default.
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- W3164644443 hasPublicationYear "2021" @default.
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