Essential meridional surfaces for tunnel number one knots

Details Essential meridional surfaces for tunnel number one knots Essential meridional surfaces for tunnel number one knots

1999-08-12

arxiv.org/abs/math/9908053v2

Bol. Soc. Mat. Mexicana (3) Vol. 6 (2000), 263-277

Mathematics

Geometric Topology

12 pages, 4 figures. Revised version

Scientific paper

We show that for each pair of positive integers g and n, there are infinitely
many tunnel number one knots, whose exteriors contain an essential meridional
surface of genus g, and with 2n boundary components. We also show that for each
positive integer n, there are tunnel number one knots whose exteriors contain n
disjoint, non-parallel, closed incompressible surfaces, each of genus n.

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