Rational structures on 3-manifolds

Selman Akbulut and Henry Churchill King

Vol. 150 (1991), No. 2, 201–214

DOI: 10.2140/pjm.1991.150.201

Abstract

In this paper we prove a conjecture of Nash for 3-manifolds. That is, we show that any two 3-manifolds are rationally equivalent. This means that by operations of topologically blowing up along smooth submanifolds (i.e. points and curves in this case) we can make any two 3-manifolds diffeomorphic to each other.

Mathematical Subject Classification 2000

Primary: 57R99

Secondary: 14P99

Milestones

Received: 1 February 1990

Revised: 30 April 1990

Published: 1 October 1991