Decompositions of 3-manifolds and pseudo-isotopies

Abstract

In this paper we construct pseudo-isotopies which realize certain cellular decompositions of 3-manifolds. In general we show that the pseudo-isotopy may be defined so as to leave points fixed outside of a given open set containing the nondegenerate elements of the decomposition. For nondegenerately continuous decompositions it is shown that the pseudo-isotopy does not move the nondegenerate elements far from their original positions.