In mathematics, the curve complex is a simplicial complex C(S) associated to a finite-type surface S, which encodes the combinatorics of simple closed curves on S. The curve complex turned out to be a fundamental tool in the study of the geometry of the Teichmüller space, of mapping class groups and of Kleinian groups. It was introduced by W.J.Harvey in 1978.
mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective...
topological curves. When complex zeros are considered, one has a complex algebraic curve, which, from the topological point of view, is not a curve, but a...
curve. Topologically, a complex elliptic curve is a torus, while a complex ellipse is a sphere. Although the formal definition of an elliptic curve requires...
complex analysis, geometric topology, differential geometry, and physics (such as in string theory). Suppose we are given a closed, oriented curve in...
where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used; contour...
smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. Plane curves also include the Jordan curves (curves that enclose...
geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H...
In complex analysis a contour is a type of curve in the complex plane. In contour integration, contours provide a precise definition of the curves on...
Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the complex plane plus one point at infinity. This extended...
this paragraph with a slightly different complex instead of the curvecomplex, called the cut system complex. An example of a relation between Dehn twists...
the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or surface is contained...
geometry, a pseudoholomorphic curve (or J-holomorphic curve) is a smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy–Riemann...
Laffer curve illustrates a theoretical relationship between rates of taxation and the resulting levels of the government's tax revenue. The Laffer curve assumes...
A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems. The...
In analytical chemistry, a calibration curve, also known as a standard curve, is a general method for determining the concentration of a substance in...
A Lissajous curve /ˈlɪsəʒuː/, also known as Lissajous figure or Bowditch curve /ˈbaʊdɪtʃ/, is the graph of a system of parametric equations x = A sin ...
In mathematics, the Fermat curve is the algebraic curve in the complex projective plane defined in homogeneous coordinates (X:Y:Z) by the Fermat equation:...
the free factor complex (sometimes also called the complex of free factors) is a free group counterpart of the notion of the curvecomplex of a finite type...
The idea is that one can extend a complex-analytic function (from here on called simply analytic function) along curves starting in the original domain...
In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers. Put another way...
the j-invariant for which a complex elliptic curve has complex multiplication. The complex elliptic curves with complex multiplication are those for...
a complexcurve, that is complex analytic manifold of dimension one (over the complex numbers). The simplest examples of such curves are the complex plane...
A learning curve is a graphical representation of the relationship between how proficient people are at a task and the amount of experience they have...
abelian variety is the same as that of elliptic curve, and every complex torus gives rise to such a curve; for g > 1 it has been known since Riemann that...
modular curves are part of the larger theory of modular curves. In particular it has another expression as a compactified quotient of the complex upper...
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