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An embedding is a representation of a topological object, manifold, graph, field, etc. in a certain space in such a way that its connectivity or algebraic properties are ...

A diagram lemma which states that, given the commutative diagram of additive Abelian groups with exact rows, the following holds: 1. If f_0 is surjective, and f_1 and f_3 are ...

There are three types of so-called fundamental forms. The most important are the first and second (since the third can be expressed in terms of these). The fundamental forms ...

Given a compact manifold M and a transversely orientable codimension-one foliation F on M which is tangent to partialM, the pair (M,F) is called a generalized Reeb component ...

Two mathematical objects are said to be homotopic if one can be continuously deformed into the other. For example, the real line is homotopic to a single point, as is any ...

An interval is a connected portion of the real line. If the endpoints a and b are finite and are included, the interval is called closed and is denoted [a,b]. If the ...

A collection of identities which hold on a Kähler manifold, also called the Hodge identities. Let omega be a Kähler form, d=partial+partial^_ be the exterior derivative, ...

The Kronecker-Weber theorem, sometimes known as the Kronecker-Weber-Hilbert theorem, is one of the earliest known results in class field theory. In layman's terms, the ...

A grand unified theory of mathematics which includes the search for a generalization of Artin reciprocity (known as Langlands reciprocity) to non-Abelian Galois extensions of ...

The lattice method is an alternative to long multiplication for numbers. In this approach, a lattice is first constructed, sized to fit the numbers being multiplied. If we ...