Tye Lidman
North Carolina State University
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Publication
Featured researches published by Tye Lidman.
Algebraic & Geometric Topology | 2013
Adam Clay; Tye Lidman; Liam Watson
We show that every irreducible toroidal integer homology sphere graph manifold has a left-orderable fundamental group. This is established by way of a specialization of a result due to Bludov and Glass [Proc. Lond. Math. Soc. 99 (2009) 585–608] for the amalgamated products that arise, and in this setting work of Boyer, Rolfsen and Wiest [Ann. Inst. Fourier (Grenoble) 55 (2005) 243–288] may be applied. Our result then depends on known relations between the topology of Seifert fibred spaces and the orderability of their fundamental groups.
Algebraic & Geometric Topology | 2015
Jennifer Hom; Tye Lidman; Faramarz Vafaee
Let P(K) be a satellite knot where the pattern P is a Berge–Gabai knot (ie a knot in the solid torus with a nontrivial solid torus Dehn surgery) and the companion K is a nontrivial knot in S^3. We prove that P(K) is an L–space knot if and only if K is an L–space knot and P is sufficiently positively twisted relative to the genus of K. This generalizes the result for cables due to Hedden [Int. Math. Res. Not. 2009 (2009) 2248–2274] and Hom [Algebr. Geom. Topol. 11 (2011) 219–223].
Compositio Mathematica | 2016
Tye Lidman; Steven Sivek
We apply results from both contact topology and exceptional surgery theory to study when Legendrian surgery on a knot yields a reducible manifold. As an application, we show that a reducible surgery on a non-cabled positive knot of genus g must have slope 2g-1, leading to a proof of the cabling conjecture for positive knots of genus 2. Our techniques also produce bounds on the maximum Thurston-Bennequin numbers of cables.
arXiv: Geometric Topology | 2017
Tye Lidman; Steven Sivek
Quasi-alternating links of determinant 1, 2, 3, and 5 were previously classified by Greene and Teragaito, who showed that the only such links are two-bridge. In this paper, we extend this result by showing that all quasi-alternating links of determinant at most 7 are connected sums of two-bridge links, which is optimal since there are quasi-alternating links not of this form for all larger determinants. We achieve this by studying their branched double covers and characterizing distance-one surgeries between lens spaces of small order, leading to a classification of formal L-spaces with order at most 7.
Pacific Journal of Mathematics | 2014
Tye Lidman; Liam Watson
We construct an infinite family of knots in rational homology spheres with irreducible, nonfibered complements, for which every nonlongitudinal filling is an L-space.
Michigan Mathematical Journal | 2016
Tye Lidman; Allison H. Moore
Mathematical Research Letters | 2015
Jennifer Hom; Tye Lidman; Nicholas Zufelt
arXiv: Geometric Topology | 2014
Cameron McA. Gordon; Tye Lidman
Geometry & Topology | 2016
Jennifer Hom; Cagri Karakurt; Tye Lidman
arXiv: Geometric Topology | 2016
Tye Lidman; Ciprian Manolescu