Double branched covers and pretzel knots

Richard Eugene Bedient

Vol. 112 (1984), No. 2, 265–272

DOI: 10.2140/pjm.1984.112.265

Abstract

Given a knot K we describe a modification of K which leaves the double branched cover of S³ branched along K unchanged. We then modify certain pretzel knots in this way to produce arbitrarily large families of distinct knots having the property that all of the associated double branched covers are homeomorphic.

Mathematical Subject Classification 2000

Primary: 57M25

Milestones

Received: 4 June 1982

Revised: 29 November 1982

Published: 1 June 1984