How do autodiffeomorphisms act on embeddings
Abstract
We work in the smooth category. The following problem was suggested by E. Rees in 2002: describe the precomposition action of selfdiffeomorphisms of S^p x S^q on the set of isotopy classes of embeddings S^p x S^q > R^m. Let g : S^p x S^q > R^m be an embedding such that g _{a x S^q} : a x S^q > R^m  g (b x S^q) is nullhomotopic for some pair of different points a,b in S^p. Theorem. If h is an autodiffeomorphism of S^p x S^q identical on a neighborhood of a x S^q for some a\in S^p and p<q and 2m<3p+3q+5, then g h is isotopic to g. Let N be an oriented (p+q)manifold and f : N > R^m, g : S^p x S^q > R^m isotopy classes of embeddings. As a corollary we obtain that under certain conditions for orientationpreserving embeddings s : S^p x D^q > N the S^pparametric embedded connected sum f#_sg depends only on f,g and the homology class of s_{S^p x 0}.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.1853
 Bibcode:
 2014arXiv1402.1853S
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Algebraic Topology;
 57R40;
 57Q37
 EPrint:
 12 pages, no figures, exposition improved