punctured torus
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Torus — Not to be confused with Taurus (disambiguation). This article is about the surface and mathematical concept of a torus. For other uses, see Torus (disambiguation). A torus As the distance to th … Wikipedia
Allen Hatcher — Allen Edward Hatcher is an American topologist and also a noted author. His book Algebraic Topology , which is the first in a series, is considered by many to be one of the best introductions to the subject.He received his Ph.D. under the… … Wikipedia
Alexander horned sphere — The Alexander horned sphere is one of the most famous pathological examples in mathematics discovered in 1924 by J. W. Alexander. It is the particular embedding of a sphere in 3 dimensional Euclidean space obtained by the following construction,… … Wikipedia
Bers slice — In the mathematical theory of Kleinian groups, Bers slices and Maskit slices, named after Lipman Bers and Bernard Maskit, are certain slices through the moduli space of Kleinian groups. Contents 1 Bers slices 2 Maskit slices 3 References … Wikipedia
Trefoil knot — In knot theory, the trefoil knot is the simplest nontrivial knot. It can be obtained by joining the loose ends of an overhand knot. It can be described as a (2,3) torus knot, and is the closure of the 2 stranded braid σ1³. It is also the… … Wikipedia
Seifert surface — In mathematics, a Seifert surface is a surface whose boundary is a given knot or link. Such surfaces can be used to study the properties of the associated knot or link. For example, many knot invariants are most easily calculated using a Seifert… … Wikipedia
Costa's minimal surface — Costa s minimal surface, cropped by a sphere. Higher resolution video In mathematics, Costa s minimal surface is an embedded minimal surface and was discovered in 1982 by the Brazilian mathematician Celso Costa. It is also a surface of finite… … Wikipedia
McShane's identity — In geometric topology, McShane s identity for a once punctured torus with a complete, finite volume hyperbolic structure is given by The sum is over all simple closed geodesics γ on the torus; here l(γ) denotes the hyperbolic length of γ.… … Wikipedia
William Floyd (mathematician) — William Floyd is an American mathematician specializing in topology. He is currently a professor at Virginia Polytechnic Institute and State University. He and Allen Hatcher classified all the incompressible surfaces in punctured torus bundles… … Wikipedia
Riemann surface — For the Riemann surface of a subring of a field, see Zariski–Riemann space. Riemann surface for the function ƒ(z) = √z. The two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real… … Wikipedia
De Rham cohomology — For Grothendieck s algebraic de Rham cohomology see Crystalline cohomology. In mathematics, de Rham cohomology (after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic… … Wikipedia
