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S-equivalence of integral Seifert matrices
Definition
Let be an even-order square matrix with integer entries, of size . A unimodular congruence replaces by for an integer matrix with determinant or . For as column vectors and , the two elementary enlargements of are Two even-order integral matrices are S-equivalent if one can be obtained from the other by a finite sequence of unimodular congruences, elementary enlargements, and reverse elementary enlargements.
Used by
- Levine–Tristram Hermitian form and signature Definition
- S-equivalence and Conway normalization Definition
- An elementary Seifert enlargement preserves the algebraic concordance class Lemma
- Seifert matrices of a knot are S-equivalent Lemma
- Seifert matrices of ambient-isotopic pairs are S-equivalent Lemma
- Seifert stabilization preserves the Levine–Tristram signature Lemma
- The Seifert form gives a quadratic enhancement and basis-independent Arf value Lemma
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.
Sources
- Dale Rolfsen, Knots and Links, Chapter 8.A–8.B (standard reference, not scraped)
- Alessia Cattabriga and Stefano Francaviglia, Knot Theory and Applications: Lecture Notes, Section 6.2.3 (standard reference, not scraped)
- Knot Theory Lecture Notes, Chapter 7: Seifert Matrices and Derived Invariants (standard reference, not scraped)
- Knot Theory Lecture Notes, Chapter 7: Seifert Matrices and Derived Invariants (standard reference, not scraped)