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

Enrique Ramírez-Losada, Luis G. Valdez-Sánchez

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 admi…