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Any link can be represented by a closed braid.

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general ...

The order ideal in Lambda, the ring of integral laurent polynomials, associated with an Alexander matrix for a knot K. Any generator of a principal Alexander ideal is called ...

An Alexander matrix is a presentation matrix for the Alexander invariant H_1(X^~) of a knot K. If V is a Seifert matrix for a tame knot K in S^3, then V^(T)-tV and V-tV^(T) ...

The Alexander polynomial is a knot invariant discovered in 1923 by J. W. Alexander (Alexander 1928). The Alexander polynomial remained the only known knot polynomial until ...

The Alexander invariant H_*(X^~) of a knot K is the homology of the infinite cyclic cover of the complement of K, considered as a module over Lambda, the ring of integral ...

A fundamental result of de Rham cohomology is that the kth de Rham cohomology vector space of a manifold M is canonically isomorphic to the Alexander-Spanier cohomology ...

The above topological structure, composed of a countable union of compact sets, is called Alexander's horned sphere. It is homeomorphic with the ball B^3, and its boundary is ...

The converse of Fisher's theorem.

There are several theorems that generally are known by the generic name "Pappus's Theorem." They include Pappus's centroid theorem, the Pappus chain, Pappus's harmonic ...