Volume 7, issue 4 (2007)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Lens spaces obtainable by surgery on doubly primitive knots

Kazuhiro Ichihara and Toshio Saito

Algebraic & Geometric Topology 7 (2007) 1949–1962

arXiv: 0708.3347

Abstract

In this paper, we consider which lens spaces are obtainable by Dehn surgery described by Berge on doubly primitive knots. An algorithm is given to decide whether a given lens space is obtainable by such a surgery. Also included is a complete characterization of such surgeries yielding lens spaces with Klein bottles.

Keywords
lens space surgery, doubly primitive knot
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27
References
Publication
Received: 29 August 2007
Accepted: 26 October 2007
Published: 18 December 2007
Authors
Kazuhiro Ichihara
School of Mathematics Education
Nara University of Education
Takabatake-cho, Nara 630-8528
Japan
http://mailsrv.nara-edu.ac.jp/~ichihara/index.html
Toshio Saito
Graduate School of Humanities and Sciences
Nara Women’s University
Kitauoyanishi-machi, Nara 630-8506
Japan