Comparing 2-handle additions to a genus 2 boundary component

Scott A. Taylor

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arXiv · 0806.1572

Comparing 2-handle additions to a genus 2 boundary component

Scott A. Taylor

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Abstract

We prove that knots obtained by attaching a band to a split link satisfy the cabling conjecture. We also give new proofs that unknotting number one knots are prime and that genus is superadditive under band sum. Additionally, we prove a collection of results comparing two 2-handle additions to a genus two boundary component of a compact, orientable 3-manifold. These results give a near complete solution to a conjecture of Scharlemann and provide evidence for a conjecture of Scharlemann and Wu. The proofs make use of a new theorem concerning the effects of attaching a 2-handle to a suture in the boundary of a sutured manifold.

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Scott A. Taylor. 2011-09-24. Comparing 2-handle additions to a genus 2 boundary component. https://arxiv.org/abs/0806.1572

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