# Signature

The signature of a knot, σ(K), is equal to σ(V + V^{t}),
the signature of V + V^{t} where V is a Seifert
matrix for the knot and V^{t} is its transpose. The knot's signature also equals the signature of the
intersection form on H_{2}(W), where W is the two-fold branched cover of
D^{4} 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

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

[2] Rolfsen, D., *Knots and Links,* AMS Chelsea Publishing, Providence (2003).

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