Classification of genus two knots which admit a (1,1) decomposition
classification
🧮 math.GT
keywords
genusknotsconsistsadmitbandingsbridgenumbervertical
read the original 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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