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

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

2008-12-16

arxiv.org/abs/0812.3086v1

Mathematics

Geometric Topology

31 pages, 11 figures. To appear in Topology and its Applications (2008)

Scientific paper

10.1016/j.topol.2008.12.031

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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