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A representation of a group G is a group action of G on a vector space V by invertible linear maps. For example, the group of two elements Z_2={0,1} has a representation phi ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

One of the three standard tori given by the parametric equations x = a(1+cosv)cosu (1) y = a(1+cosv)sinu (2) z = asinv, (3) corresponding to the torus with a=c. It has ...

An operation on rings and modules. Given a commutative unit ring R, and a subset S of R, closed under multiplication, such that 1 in S, and 0 not in S, the localization of R ...

Noncommutative topology is a recent program having important and deep applications in several branches of mathematics and mathematical physics. Because every commutative ...

The concept of a space is an extremely general and important mathematical construct. Members of the space obey certain addition properties. Spaces which have been ...

There are two incompatible definitions of the squircle. The first defines the squircle as the quartic plane curve which is special case of the superellipse with a=b and r=4, ...

The trapezo-rhombic dodecahedron, also called the rhombo-trapezoidal dodecahedron, is a general dodecahedron consisting of six identical rhombi and six identical isosceles ...

The wedge product is the product in an exterior algebra. If alpha and beta are differential k-forms of degrees p and q, respectively, then alpha ^ beta=(-1)^(pq)beta ^ alpha. ...

A Latin square is said to be odd if it contains an odd number of rows and columns that are odd permutations. Otherwise, it is said to be even. Let the number of even Latin ...