Knots of genus one or on the number of alternating knots of given genus

Stoimenow, A.

doi:10.1090/S0002-9939-01-05823-3

Knots of genus one or on the number of alternating knots of given genus
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Proc. Amer. Math. Soc. 129 (2001), 2141-2156 Request permission

Abstract:

We prove that any non-hyperbolic genus one knot except the trefoil does not have a minimal canonical Seifert surface and that there are only polynomially many in the crossing number positive knots of given genus or given unknotting number.

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