Restricting isotopies of spheres

Jospeh Atkins Childress, Jr.

Vol. 45 (1973), No. 2, 415–418

DOI: 10.2140/pjm.1973.45.415

Abstract

In this note we consider the problem of determining whether isotopic homeomorphisms of Sⁿ that agree on a subset X of Sⁿ are isotopic by an isotopy that is fixed on X. In particular, in the PL category, an affirmative answer is obtained for X a locally unknotted closed cell or an unknotted sphere.

Mathematical Subject Classification

Primary: 57C25

Secondary: 57C35

Milestones

Received: 11 November 1971

Published: 1 April 1973