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    Seifert Matrix

    Definition

    Given a Seifert form f(x, y), choose a basis e_1, ..., e_(2g) for H_1(M^^) as a Z-module so every element is uniquely expressible as n_1 e_1 + ... + n_(2g) e_(2g) with n_i integer. Then define the Seifert matrix V as the 2g×2g integer matrix with entries v_(i j) = lk(e_i, e_j^+). For example, the right-hand trefoil knot has Seifert matrix V = [-1 | 1 0 | -1].

    Related term

    Alexander matrix

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