Crosscap number two knots in $S^3$ with (1,1) decompositions

Enrique Ramírez-Losada; Luis G. Valdez-Sánchez

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Crosscap number two knots in $S^3$ with (1,1) decompositions

Enrique Ramírez-Losada·Luis G. Valdez-Sánchez

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Abstract

M. Scharlemann has recently proved that any genus one tunnel number one knot is either a satellite or 2-bridge knot, as conjectured by H. Goda and M. Teragaito; all such knots admit a (1,1) decomposition. In this paper we give a classification of the family of (1,1) knots in $S^3$ with crosscap number two (i.e., bounding an essential once-punctured Klein bottle).

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Enrique Ramírez-Losada, Luis G. Valdez-Sánchez. 2005-10-31. Crosscap number two knots in $S^3$ with (1,1) decompositions. https://arxiv.org/abs/math/0511005

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