Volume 16, issue 3 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25, 1 issue

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
L-space surgery and twisting operation

Kimihiko Motegi

Algebraic & Geometric Topology 16 (2016) 1727–1772
Abstract

A knot in the 3–sphere is called an L-space knot if it admits a nontrivial Dehn surgery yielding an L-space, ie a rational homology 3–sphere with the smallest possible Heegaard Floer homology. Given a knot K, take an unknotted circle c and twist K n times along c to obtain a twist family {Kn}. We give a sufficient condition for {Kn} to contain infinitely many L-space knots. As an application we show that for each torus knot and each hyperbolic Berge knot K, we can take c so that the twist family {Kn} contains infinitely many hyperbolic L-space knots. We also demonstrate that there is a twist family of hyperbolic L-space knots each member of which has tunnel number greater than one.

Keywords
L-space surgery, L-space knot, twisting, seiferter, tunnel number
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Secondary: 57N10
References
Publication
Received: 28 April 2015
Revised: 16 August 2015
Accepted: 10 September 2015
Published: 1 July 2016
Authors
Kimihiko Motegi
Department of Mathematics
Nihon University
3-25-40 Sakurajosui, Setagaya-ku
Tokyo 156-8550
Japan
http://www.math.chs.nihon-u.ac.jp/~motegi/