Search Results for ""

Milnor (1956) found more than one smooth structure on the seven-dimensional hypersphere. Generalizations have subsequently been found in other dimensions. Using surgery ...

A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

The Smale horseshoe map consists of a sequence of operations on the unit square. First, stretch in the y direction by more than a factor of two, then compress in the x ...

An Abelian variety is an algebraic group which is a complete algebraic variety. An Abelian variety of dimension 1 is an elliptic curve.

If two projective pencils of curves of orders n and n^' have no common curve, the locus of the intersections of corresponding curves of the two is a curve of order n+n^' ...

A notation used to describe curves. The fundamental principle of Clebsch-Aronhold notation states that if each of a number of forms be replaced by a power of a linear form in ...

Two elements alpha, beta of a field K, which is an extension field of a field F, are called conjugate (over F) if they are both algebraic over F and have the same minimal ...

Let s_i be the orders of singular points on a curve (Coolidge 1959, p. 56). Harnack's first theorem states that a real irreducible curve of order n cannot have more than ...

A quartic algebraic curve also called the peg-top curve and given by the Cartesian equation a^4y^2=b^2x^3(2a-x) (1) and the parametric curves x = a(1+sint) (2) y = ...

A generalization to a quartic three-dimensional surface is the quartic surface of revolution (x^4-ax^3)+a^2(y^2+z^2)=0, (1) illustrated above. With a=1, this surface is ...