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Seifert Matrix

المؤلف:  Rolfsen, D

المصدر:  Knots and Links. Wilmington, DE: Publish or Perish Press

الجزء والصفحة:  pp. 200-203

9-6-2021

2670

Seifert Matrix

Given a Seifert form , choose a basis , ...,  for  as a -module so every element is uniquely expressible as

(1)

with  integer. Then define the Seifert matrix  as the  integer matrix with entries

(2)

For example, the right-hand trefoil knot has Seifert matrix

(3)

A Seifert matrix is not a knot invariant, but it can be used to distinguish between different Seifert surfaces for a given knot.

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REFERENCES:

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 200-203, 1976.