Classification of genus two knots which admit a (1,1) decomposition

2016/03/28 by Eudave-Muñoz, Mario, Manjarrez-Gutierrez, Fabiola, Ramirez-Losada, Enrique
#57M25 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1603.08418

Abstract

We describe the genus two knots which admit a genus one, one bridge position. These are divided into several families, one consists of vertical bandings of two genus one (1,1)-knots, other consists of vertical bandings of two cross cap number two 2-bridge knots, and the last one consists of genus two tunnel number one satellite knots.

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