embedding problem

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• Embedding problem — In Galois theory, a branch of mathematics, the embedding problem is a generalization of the inverse Galois problem. Roughly speaking, it asks whether a given Galois extension can be embedded into a Galois extension in such a way that the… …   Wikipedia

• Connes embedding problem — In von Neumann algebras, the Connes embedding problem or conjecture, due to Alain Connes, asks whether every type II1 factor on a separable Hilbert space can be embedded into the ultrapower of the hyperfinite type II1 factor by a free ultrafilter …   Wikipedia

• Nash embedding theorem — The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded into some Euclidean space. Isometric means preserving the length of every path. For instance,… …   Wikipedia

• Post correspondence problem — The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post in 1946.[1] Because it is simpler than the halting problem and the Entscheidungsproblem it is often used in proofs of undecidability. Contents 1… …   Wikipedia

• Word problem for groups — In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a recursively presented group G is the algorithmic problem of deciding whether two words represent the same element. Although it… …   Wikipedia

• Graph embedding — In topological graph theory, an embedding of a graph G on a surface Sigma; is a representation of G on Sigma; in which points of Sigma; are associated to vertices and simple arcs (homeomorphic images of [0,1] ) are associated to edges in such a… …   Wikipedia

• Book embedding — In graph theory, book embedding is a generalization of planar embedding to nonplanar surfaces in the form of a book , a collection of pages (halfplanes) joined together at the spine of the book (the shared boundary of all the halfplanes). The… …   Wikipedia

• Higman's embedding theorem — In group theory, Higman s embedding theorem states that every finitely generated recursively presented group R can be embedded as a subgroup of some finitely presented group G . This is a result of Graham Higman from the 1960s. [ Graham Higman,… …   Wikipedia

• Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

• Topological graph theory — In mathematics topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, and graphs as topological spaces. [J.L. Gross and T.W. Tucker, Topological graph theory, Wiley Interscience, 1987] Embedding a… …   Wikipedia

• graph theory — Math. the branch of mathematics dealing with linear graphs. [1965 70] * * * Mathematical theory of networks. A graph consists of nodes (also called points or vertices) and edges (lines) connecting certain pairs of nodes. An edge that connects a… …   Universalium