## Illinois Journal of Mathematics

- Illinois J. Math.
- Volume 51, Number 3 (2007), 937-950.

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

#### 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 $S^p\times S^p$, respectively, and we determine the algebraic structure of such subgroups when $n>4$ and $p>1$.

#### Article information

**Source**

Illinois J. Math., Volume 51, Number 3 (2007), 937-950.

**Dates**

First available in Project Euclid: 13 November 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.ijm/1258131112

**Digital Object Identifier**

doi:10.1215/ijm/1258131112

**Mathematical Reviews number (MathSciNet)**

MR2379732

**Zentralblatt MATH identifier**

1153.57020

**Subjects**

Primary: 57N37: Isotopy and pseudo-isotopy

Secondary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25} 57R50: Diffeomorphisms

#### Citation

Krylov, Nikolai A. Pseudo-isotopy classes of diffeomorphisms of the unknotted pairs $(S\sp {n+2},S\sp n)$ and $(S\sp {2p+2},S\sp p\times S\sp p)$. Illinois J. Math. 51 (2007), no. 3, 937--950. doi:10.1215/ijm/1258131112. https://projecteuclid.org/euclid.ijm/1258131112