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

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).

16 pages, 11 figures, to appear in {\it Boletín de la Sociedad Matemática Mexicana,} FicoFest Proceedings

Cited by in corpus (1)

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