 Alexander breadth bound on Seifert genus

ID: alexander-breadth-bound-on-seifert-genus

2 g_{s} (K)

-by-

2 g_{s} (K)

V

. Each entry of

t V - V^{T}

has degree at most one, so its determinant has breadth of a Laurent polynomial at most

2 g_{s} (K)

. This lower bound on Seifert genus need not be sharp: an untwisted Whitehead double can have Alexander polynomial of a knot

1

and positive Seifert genus.

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