Hyperbolic (1,2)-knots in S^3 with crosscap number two and tunnel number one
arXiv:0812.3086 · doi:10.1016/j.topol.2008.12.031
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.
31 pages, 11 figures. To appear in Topology and its Applications (2008)