Closed essential surfaces in the complements of large volume Berge knots

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We construct an algorithm that lists all closed essential surfaces in the complement of a knot that lies on the fiber of a trefoil or figure eight knot. Such knots are Berge knots and hence admit lens space surgeries. Furthermore they may have arbitrarily large hyperbolic volume. Using this algorithm we concoct large volume Berge knots of two flavors: those whose complement contains arbitrarily many distinct closed essential surfaces, and those whose complement contains no closed essential surfaces.
41 pages, 11 figures

Keywords

Geometric Topology, 57M50 (Primary), 57M25 (Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/76257

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509082
 http://arxiv.org/abs/math/0509082

Collections

arXiv