Representing codimension-one homology classes by embedded submanifolds

William H. Meeks, III and Julie Patrusky

Vol. 68 (1977), No. 1, 175–176

DOI: 10.2140/pjm.1977.68.175

Abstract

In this paper we prove a general theorem on representing codimension-one homology classes on compact manifolds. Our theorem gives an elementary proof of the classical result that a one-dimensional homology class on a compact orientable surface can be represented by an embedded circle precisely when the class is primitive. We will call a komology class primitive if it is the zero class or if it is nol a nontrivial multiple of another class.

Mathematical Subject Classification

Primary: 57D95, 57D95

Milestones

Received: 12 December 1974

Revised: 23 July 1976

Published: 1 January 1977