Signature

A signature (/ˈsɪɡnətʃər/; from Latin: signare, "to sign") is a handwritten (and often stylized) depiction of someone's name, nickname, or even a simple "X" or other mark that a person writes on documents as a proof of identity and intent. The writer of a signature is a signatory or signer. Similar to a handwritten signature, a signature work describes the work as readily identifying its creator. A signature may be confused with an autograph, which is chiefly an artistic signature. This can lead to confusion when people have both an autograph and signature and as such some people in the public eye keep their signatures private whilst fully publishing their autograph.

Function and types

The traditional function of a signature is evidential: it is to give evidence of:

For example, the role of a signature in many consumer contracts is not solely to provide evidence of the identity of the contracting party, but also to provide evidence of deliberation and informed consent.

Signature (disambiguation)

A signature is a hand-written, possibly stylized, version of someone's name, which may be used to confirm the person's identity. The writer of a signature is a signatory or signer.

Signature or signatory may also refer to:

In art:

In computing:

In cryptography:

Signature (topology)

In the mathematical field of topology, the signature is an integer invariant which is defined for an oriented manifold M of dimension d=4k divisible by four (doubly even-dimensional).

This invariant of a manifold has been studied in detail, starting with Rokhlin's theorem for 4-manifolds.

Definition

Given a connected and oriented manifold M of dimension 4k, the cup product gives rise to a quadratic form Q on the 'middle' real cohomology group

The basic identity for the cup product

shows that with p = q = 2k the product is symmetric. It takes values in

If we assume also that M is compact, Poincaré duality identifies this with

which can be identified with Z. Therefore cup product, under these hypotheses, does give rise to a symmetric bilinear form on H^2k(M,Z); and therefore to a quadratic form Q. The form Q is non-degenerate due to Poincaré duality, as it pairs non-degenerately with itself. More generally, the signature can be defined in this way for any general compact polyhedron with 4n-dimensional Poincaré duality.