signature of a knot
The signature of a knot is a topological invariant in knot theory. It may be computed from the Seifert surface.
Given a knot K in the 3-sphere, it has a
Seifert surface S whose boundary is K. The Seifert form of S is the
pairing 
given by taking the linking number
lk(a + ,b - ) where 
and a
+ ,b - indicate the translates of a and b respectively in the positive and
negative directions of the normal bundle to S.
Given a basis b1,...,b2g for H1(S) (where g is the genus of the surface) the Seifert form can be represented
as a 2g-by-2g Seifert matrix V, Vij = φ(bi,bj). The
signature of the matrix 
, thought of as a symmetric bilinear form, is
the signature of the knot K.
Slice knots have zero signature and so play an important role in the theory.
See also
- Link concordance
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