SU(2)-cyclic surgeries and the pillowcase

Steven Sivek; Raphael Zentner

doi:10.4310/jdg/1656005497

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arXiv · 1710.01957

SU(2)-cyclic surgeries and the pillowcase

Steven Sivek·Raphael Zentner

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Abstract

We study knots in $S^3$ with infinitely many $SU(2)$-cyclic surgeries, which are Dehn surgeries such that every representation of the resulting fundamental group into $SU(2)$ has cyclic image. We show that for every such nontrivial knot $K$, its set of $SU(2)$-cyclic slopes is bounded and has a unique limit point, which is both a rational number and a boundary slope for $K$. We also show that such knots are prime and have infinitely many instanton L-space surgeries. Our methods include the application of holonomy perturbation techniques to instanton knot homology, using a strengthening of recent work by the second author.

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BibTeX RIS

Steven Sivek, Raphael Zentner. 2017-10-05. SU(2)-cyclic surgeries and the pillowcase. https://doi.org/10.4310/jdg%2F1656005497

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