Vol. 284, No. 1, 2016

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ISSN: 0030-8730
Bitwist manifolds and two-bridge knots

James W. Cannon, William J. Floyd, LeeR Lambert, Walter R. Parry and Jessica S. Purcell

Vol. 284 (2016), No. 1, 1–39
Abstract

We give uniform, explicit, and simple face-pairing descriptions of all the branched cyclic covers of the 3-sphere, branched over two-bridge knots. Our method is to use the bitwisted face-pairing constructions of Cannon, Floyd, and Parry; these examples show that the bitwist construction is often efficient and natural. Finally, we give applications to computations of fundamental groups and homology of these branched cyclic covers.

Though LeeR Lambert spent his life as an actuary and a musician and was a loving \null father of nine girls and one boy, he had always wanted to earn an advanced degree as a mathematician. With the encouragement of his wife, he earned his Ph.D. in mathematics at the age of 68. Many of the results of this paper appeared in his Ph.D. dissertation at Brigham Young University. At the age of 71, LeeR died of bone cancer. We miss you, LeeR. \rightskip=14pt \leftskip=14pt

Keywords
bitwist manifolds, two-bridge knots, branched cyclic covers
Mathematical Subject Classification 2010
Primary: 57M12, 57M25
Milestones
Received: 26 May 2015
Revised: 28 January 2016
Accepted: 18 February 2016
Published: 10 July 2016
Authors
James W. Cannon
Department of Mathematics
Brigham Young University
279 TMCB
Provo, UT 84602
United States
William J. Floyd
Department of Mathematics
Virginia Tech
Blacksburg, VA 24061
United States
LeeR Lambert
Department of Mathematics
Brigham Young University
Provo, UT 84602
United States
Walter R. Parry
Department of Mathematics
Eastern Michigan University
Ypsilanti, MI 48197
United States
Jessica S. Purcell
School of Mathematical Sciences
Monash University
9 Rainforest Walk, Room 401
Clayton, VIC 3800
Australia