TL;DR
This paper surveys a specialized area in Knot Theory focusing on surfaces within knot exteriors, discussing conjectures and their solutions or counterexamples, providing insights into the structure of knots and related surfaces.
Contribution
It offers a comprehensive survey of surfaces in knot exteriors and updates on conjectures with new comments on their solutions or counterexamples.
Findings
Added comments on solutions or counterexamples for key conjectures
Provides a detailed survey of surfaces in knot exteriors
Enhances understanding of knot structures and related conjectures
Abstract
This article is an English translation of Japanese article "Musubime to Kyokumen", Math. Soc. Japan, Sugaku Vol. 67, No. 4 (2015) 403--423. It surveys a specific area in Knot Theory concerning surfaces in knot exteriors. In version 2, we added comments on the solutions or counterexamples for Conjecture 3.5, Conjecture 3.7 and Conjecture 5.30.
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Taxonomy
TopicsMathematics and Applications · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory