Crosscap number two knots in $S^3$ with (1,1) decompositions
Geometric Topology
2016-08-16 v1
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 with crosscap number two (i.e., bounding an essential once-punctured Klein bottle).
Keywords
Cite
@article{arxiv.math/0511005,
title = {Crosscap number two knots in $S^3$ with (1,1) decompositions},
author = {Enrique Ramírez-Losada and Luis G. Valdez-Sánchez},
journal= {arXiv preprint arXiv:math/0511005},
year = {2016}
}
Comments
16 pages, 11 figures, to appear in {\it Bolet\'{i}n de la Sociedad Matem\'atica Mexicana,} FicoFest Proceedings