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The homomorphism S which, according to the snake lemma, permits construction of an exact sequence (1) from the above commutative diagram with exact rows. The homomorphism S ...

A simple way to describe a knot projection. The advantage of this notation is that it enables a knot diagram to be drawn quickly. For an oriented alternating knot with n ...

In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...

The square torus is the quotient of the plane by the integer lattice.

The word "star" is used in a number of different ways in mathematics. The term is commonly used to voice an asterisk when appearing in a mathematical expression. For example, ...

A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set ...

Graph Strength

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 class of fibered knots and links which arises in algebraic geometry. An algebraic link is formed by connecting the NW and NE strings and the SW and SE strings of an ...

An algebraic manifold is another name for a smooth algebraic variety. It can be covered by coordinate charts so that the transition functions are given by rational functions. ...