Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots - Mathematics > Geometric TopologyReportar como inadecuado




Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots - Mathematics > Geometric Topology - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: In this paper we use continued fractions to study a partial order on the setof 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. Weestablish necessary and sufficient conditions for any set of 2-bridge knots tohave an upper bound with respect to the partial order. Moreover, given any2-bridge knot K we characterize all other 2-bridge knots J such that {K, J} hasan upper bound. As an application we answer a question of Suzuki, showing thatthere is no upper bound for the set consisting of the trefoil and figure-eightknots.



Autor: Scott M. Garrabrant, Jim Hoste, Patrick D. Shanahan

Fuente: https://arxiv.org/







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