signature theorem
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Signature operator — Let X be a 4k dimensional compact Riemannian manifold. The signature operator is a elliptic differential operator defined on a subspace of the space of differential forms on X , whose analytic index is the same as the topological signature of the … Wikipedia
Signature (topology) — In mathematics, the signature of an oriented manifold M is defined when M has dimension d divisible by four. In that case, when M is connected and orientable, cup product gives rise to a quadratic form Q on the middle real cohomology group: H 2 n … Wikipedia
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 phi : H 1(S) imes … Wikipedia
Atiyah–Singer index theorem — In the mathematics of manifolds and differential operators, the Atiyah–Singer index theorem states that for an elliptic differential operator on a compact manifold, the analytical index (closely related to the dimension of the space of solutions) … Wikipedia
Rokhlin's theorem — In 4 dimensional topology, a branch of mathematics, Rokhlin s theorem states that if a smooth, compact 4 manifold M has a spin structure (or, equivalently, the second Stiefel Whitney class w 2( M ) vanishes), then the signature of its… … Wikipedia
Löwenheim–Skolem theorem — In mathematical logic, the Löwenheim–Skolem theorem, named for Leopold Löwenheim and Thoralf Skolem, states that if a countable first order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The… … Wikipedia
Metric signature — The signature of a metric tensor (or more generally a nondegenerate symmetric bilinear form, thought of as quadratic form) is the number of positive and negative eigenvalues of the metric. That is, the corresponding real symmetric matrix is… … Wikipedia
Quantum digital signature — A Quantum Digital Signature (QDS) refers to the quantum mechanical equivalent of either a classical digital signature or, more generally, a handwritten signature on a paper document. Like a handwritten signature, a digital signature is used to… … Wikipedia
Digital Signature Algorithm — The Digital Signature Algorithm (DSA) is a United States Federal Government standard or FIPS for digital signatures. It was proposed by the National Institute of Standards and Technology (NIST) in August 1991 for use in their Digital Signature… … Wikipedia
Fundamental theorem of arithmetic — In number theory, the fundamental theorem of arithmetic (or unique prime factorization theorem) states that every natural number greater than 1 can be written as a unique product of prime numbers. For instance, : 6936 = 2^3 imes 3 imes 17^2 , ,! … Wikipedia
Proof sketch for Gödel's first incompleteness theorem — This article gives a sketch of a proof of Gödel s first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses which are discussed as needed during the sketch. We will assume for the… … Wikipedia
