Hyperbolic (1,2)-knots in S^3 with crosscap number two and tunnel number one

Luis G. Valdez-Sanchez; Enrique Ramirez-Losada

doi:10.1016/j.topol.2008.12.031

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arXiv · 0812.3086

Hyperbolic (1,2)-knots in S^3 with crosscap number two and tunnel number one

Luis G. Valdez-Sanchez·Enrique Ramirez-Losada

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Abstract

A knot in S^3 is said to have crosscap number two if it bounds a once-punctured Klein bottle but not a Moebius band. In this paper we give a method of constructing crosscap number two hyperbolic (1,2)-knots with tunnel number one which are neither 2-bridge nor (1,1)-knots. An explicit infinite family of such knots is discussed in detail.

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Luis G. Valdez-Sanchez, Enrique Ramirez-Losada. 2008-12-16. Hyperbolic (1,2)-knots in S^3 with crosscap number two and tunnel number one. https://doi.org/10.1016/j.topol.2008.12.031

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