Berge–Gabai knots and L–space satellite operations

Published

Journal Article

© 2014 Mathematical Sciences Publishers. All rights reserved. Let P(K) be a satellite knot where the pattern P is a Berge–Gabai knot (ie a knot in the solid torus with a nontrivial solid torus Dehn surgery) and the companion K is a nontrivial knot in S3. We prove that P(K) is an L–space knot if and only if K is an L–space knot and P is sufficiently positively twisted relative to the genus of K. This generalizes the result for cables due to Hedden [13] and Hom [17].

Full Text

Duke Authors

Cited Authors

  • Hom, J; Lidman, T; Vafaee, F

Published Date

  • January 15, 2015

Published In

Volume / Issue

  • 14 / 6

Start / End Page

  • 3745 - 3763

Electronic International Standard Serial Number (EISSN)

  • 1472-2739

International Standard Serial Number (ISSN)

  • 1472-2747

Digital Object Identifier (DOI)

  • 10.2140/agt.2014.14.3745

Citation Source

  • Scopus