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This article is available for purchase or by subscription. See below.
Abstract
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We prove that if
is a nontrivial alternating link embedded (without crossings) in a closed surface
, then
has a compressing disk
whose boundary intersects
in no more than two points. Moreover, whenever the surface is incompressible and
–incompressible
in the link exterior, it can be isotoped to have a standard tube at some crossing of
any reduced alternating diagram.
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Keywords
alternating knot, alternating link, representativity,
closed surface, compressing disk
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Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M50
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Publication
Received: 24 August 2017
Revised: 4 December 2017
Accepted: 11 April 2018
Published: 18 October 2018
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