Given a Seifert Form , choose a basis , ..., for as a Z-module so every
element is uniquely expressible as
with integer, define the Seifert matrix as the integral Matrix with entries
The right-hand Trefoil Knot has Seifert matrix
A Seifert matrix is not a knot invariant, but it can be used to distinguish between different
Seifert Surfaces for a given knot.
See also Alexander Matrix
References
Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 200-203, 1976.
© 1996-9 Eric W. Weisstein
1999-05-26