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

Mario Eudave-Muñoz; Fabiola Manjarrez-Gutierrez; Enrique Ramirez-Losada

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arXiv · 1603.08418

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

Mario Eudave-Muñoz·Fabiola Manjarrez-Gutierrez·Enrique Ramirez-Losada

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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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Mario Eudave-Muñoz, Fabiola Manjarrez-Gutierrez, Enrique Ramirez-Losada. 2016-03-28. Classification of genus two knots which admit a (1,1) decomposition. https://arxiv.org/abs/1603.08418

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