Proposed Property 2R counterexamples classified

Martin Scharlemann

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arXiv · 1208.1299

Proposed Property 2R counterexamples classified

Martin Scharlemann

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Abstract

Earlier work with Robert Gompf and Abigail Thompson classified, via a natural slope indexed by the rationals, all two-component links which contain the square knot and from which $(S^1 \times S^2) \# (S^1 \times S^2)$ can be obtained by surgery. It was argued that a certain family $L_n$ of such links probably contradict the Generalized Property R Conjecture. Left unresolved was how the family $L_n$ fits into the classification scheme. This question is resolved here, in part by giving varied perspectives and more detail on the construction of the $L_n$.

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BibTeX RIS

Martin Scharlemann. 2015-09-14. Proposed Property 2R counterexamples classified. https://arxiv.org/abs/1208.1299

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