Signature


The signature of a knot, σ(K), is equal to σ(V + Vt), the signature of V + Vt where V is a Seifert Matrix for the knot. The signature also equals the signature of the intersection form on H2(W), where W is the two-fold branched cover of D4 over a pushed-in Seifert surface.

The signature provides bounds for the smooth 4-genus of a knot, for instance, slice knots have signature zero.


References

L. Kauffman, and L. Taylor, Signature of Links, Trans. Amer. Math. Soc. 216 (1976), 351-365.

D. Rolfsen, Knots and Links, AMS Chelsea Publishing, Providence (2003)