Surgery on a class of pretzel knots

William Ortmeyer

Vol. 127 (1987), No. 1, 155–171

DOI: 10.2140/pjm.1987.127.155

Abstract

Any closed 3-manifold M may be thought of as a union of 3-celIs. Any covering space of M is made up of copies of these 3-cells with boundaries locally identified as in M. Covers of M may be built by piecing together these balls. This paper develops a method to piece together the universal cover of manifolds obtained from the 3-sphere by surgery on a class of pretzel knots in such a way that the cover can be shown to be R³.

Mathematical Subject Classification 2000

Primary: 57M25

Milestones

Received: 5 June 1985

Revised: 25 March 1986

Published: 1 March 1987