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In mathematics, genus (pl.: genera) has a few different, but closely related, meanings. Intuitively, the genus is the number of "holes" of a surface . [ 1 ] A sphere has genus 0, while a torus has genus 1.
The non-negative integer = {,} is called the genus of the entire function . If the order is not an integer, then = [] is the integer part of ...
In mathematics, the genus is a classification of quadratic forms and lattices over the ring of integers. An integral quadratic form is a quadratic form on Z n, or equivalently a free Z-module of finite rank. Two such forms are in the same genus if they are equivalent over the local rings Z p for each prime p and also equivalent over R.
The curve has genus one (genus formula); in particular, it is not isomorphic to the projective line P 1, which has genus zero. Using genus to distinguish curves is very basic: in fact, the genus is the first invariant one uses to classify curves (see also the construction of moduli of algebraic curves).
In mathematics, the arithmetic genus of an algebraic variety is one of a few possible generalizations of the genus of an algebraic curve or Riemann surface.
In classical algebraic geometry, the genus–degree formula relates the degree of an irreducible plane curve with its arithmetic genus via the formula: = (). Here "plane curve" means that is a closed curve in the projective plane.
A cobordism (W; M, N).In mathematics, a genus of a multiplicative sequence is a ring homomorphism from the ring of smooth compact manifolds up to the equivalence of bounding a smooth manifold with boundary (i.e., up to suitable cobordism) to another ring, usually the rational numbers, having the property that they are constructed from a sequence of polynomials in characteristic classes that ...
genus The genus of a graph is the minimum genus of a surface onto which it can be embedded; see embedding. geodesic As a noun, a geodesic is a synonym for a shortest path. When used as an adjective, it means related to shortest paths or shortest path distances. giant