Berge–Gabai knots and L–space satellite operations
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© 2014 Mathematical Sciences Publishers. All rights reserved. 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 S3. 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  and Hom .
SubjectScience & Technology
Published Version (Please cite this version)10.2140/agt.2014.14.3745
Publication InfoVafaee, Faramarz; Hom, Jennifer; & Lidman, Tye (2015). Berge–Gabai knots and L–space satellite operations. Algebraic & Geometric Topology, 14(6). pp. 3745-3763. 10.2140/agt.2014.14.3745. Retrieved from https://hdl.handle.net/10161/17371.
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Phillip Griffiths Assistant Research Professor
My main research interests lie in low dimensional topology and geometry. Among others, these interests include Heegaard Floer homology and its applications, Khovanov homology, contact and symplectic geometry, and handlebody theory. A central goal of low dimensional topology is to understand three and four–dimensional spaces. Achieving this understanding is often aided through the study of knots and surfaces embedded therein, and the theory of knotted curves and surfaces have