TL;DR
This paper proves that for a specific class of fibered links in the 3-sphere, the unknotting tunnel can always be isotoped to lie within the fiber surface, simplifying their topological analysis.
Contribution
It establishes that the unknotting tunnel for tunnel number one fibered links can be isotoped into the fiber surface, providing new insight into their structure.
Findings
The unknotting tunnel can be isotoped into the fiber surface.
Simplifies understanding of tunnel number one fibered links.
Provides a method for isotoping tunnels in these links.
Abstract
Let K be a tunnel number one, fibered link in S^3, with fiber F, and unknotting tunnel . We show that can be isotoped to lie in F.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · semigroups and automata theory