Pseudo-isotopy classes of diffeomorphisms of the unknotted pairs \((S^{n+2},S^n)\) and \((S^{2p+2},S^p\times S^p)\)

zbMATH Open1153.57020arXivmath/0601715MaRDI QIDQ938629

Nikolai A. Krylov

Publication date: 26 August 2008

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Abstract: We consider two pairs: the standard unknotted $n$-sphere in $S^{n+2}$, and the product of two $p$-spheres trivially embedded in $S^{2p+2}$, and study orientation preserving diffeomorphisms of these pairs. Pseudo-isotopy classes of such diffeomorphisms form subgroups of the mapping class groups of $S^n$ and $S^{p}imes{S}^p$ respectively and we determine the algebraic structure of such subgroups when $n>4$ and $p>1$.

Full work available at URL: https://arxiv.org/abs/math/0601715

zbMATH Keywords

diffeomorphismknotextensionquasi-isotopy, mapping class group

Mathematics Subject Classification ID

Isotopy and pseudo-isotopy (57N37) Extension of maps (54C20) Differential topological aspects of diffeomorphisms (57R50)

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