Handle number one links and generalized property R
Michael J. Williams
TL;DR
This paper proves that links in the three-sphere with exteriors admitting a genus 2 Heegaard splitting satisfy the Generalized Property R, linking topological properties of the exterior to link properties.
Contribution
It establishes a new connection between the topology of link exteriors and the Generalized Property R, extending previous results to a broader class of links.
Findings
Links with genus 2 Heegaard exteriors have Generalized Property R.
The result generalizes known cases of Property R.
Topological conditions on the exterior imply link properties.
Abstract
It is shown that if the exterior of a link L in the three sphere admits a genus 2 Heegaard splitting, then L has Generalized Property R.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · semigroups and automata theory