Triangulations with the free cell property

William Owen Murray, IV and L. Bruce Treybig

Vol. 75 (1978), No. 2, 487–496

DOI: 10.2140/pjm.1978.75.487

Abstract

We show that if each of M₁ and M₂ is a connected, orientable, 3-manifold having a triangulation with the free cell property, then the connected sum M₁#M₂ has a natural triangulation with the free cell property. We also show that if M is a connected, orientable, 3-manifold having a triangulation with the free cell property, and a manifold N is formed from M by adding a handle, then N has a natural triangulation with the free cell property. These theorems are then applied to show that E³ and various other noncompact 3-manifolds have triangulations wilh the free cell property.

Mathematical Subject Classification 2000

Primary: 57Q05

Secondary: 57Q15

Milestones

Received: 29 October 1976

Revised: 8 June 1977

Published: 1 April 1978