Genus-2 surface

Genus-2 surface
A genus-2 surface.

In mathematics, a genus-2 surface (also known as a double torus or two-holed torus) is a surface formed by the connected sum of two tori. That is to say, from each of two tori the interior of a disk is removed, and the boundaries of the two disks are identified (glued together), forming a double torus.

This is the simplest case of the connected sum of n tori. A connected sum of tori is an example of a two dimensional manifold. According to the classification theorem for 2-manifolds, every compact connected 2-manifold is either a sphere, a connected sum of tori, or a connected sum of real projective planes.

Double torus knots are studied in knot theory.

Contents

Example

The Bolza surface is the most symmetric hyperbolic surface of genus 2.

See also

Triple torus

References

  • James R. Munkres, Topology, Second Edition, Prentice-Hall, 2000, ISBN 0-13-181629-2.
  • William S. Massey, Algebraic Topology: An Introduction, Harbrace, 1967.

External links


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Surface — This article discusses surfaces from the point of view of topology. For other uses, see Differential geometry of surfaces, algebraic surface, and Surface (disambiguation). An open surface with X , Y , and Z contours shown. In mathematics,… …   Wikipedia

  • Genus (mathematics) — In mathematics, genus has a few different, but closely related, meanings:TopologyOrientable surfaceThe genus of a connected, orientable surface is an integer representing the maximum number of cuttings along closed simple curves without rendering …   Wikipedia

  • Genus–degree formula — In classical algebraic geometry, the genus–degree formula relates the degree d of a non singular plane curve with its arithmetic genus g via the formula: A singularity of order r decreases the genus by .[1] Proofs The proof follows immediately… …   Wikipedia

  • Surface of general type — In algebraic geometry, a surface of general type is an algebraic surface with Kodaira dimension 2.These are all algebraic, and in some sense most surfaces are in this class. ClassificationGieseker showed that there is a coarse moduli scheme for… …   Wikipedia

  • Surface of class VII — In mathematics, surfaces of class VII are non algebraic complex surfaces studied by (Kodaira 1964, 1968) that have Kodaira dimension −∞ and first Betti number 1. Minimal surfaces of class VII (those with no rational curves with self… …   Wikipedia

  • Surface de Bolza — Représentation en perspective de l équation y2 = x5 − x dans . En mathématiques, la surface de Bolza (du nom d Oskar Bolza) est une surface de Riemann compacte de g …   Wikipédia en Français

  • genus Culex — noun type genus of the Culicidae: widespread genus of mosquitoes distinguished by holding the body parallel to the resting surface • Syn: ↑Culex • Hypernyms: ↑arthropod genus • Member Holonyms: ↑Culicidae, ↑family Culicidae …   Useful english dictionary

  • genus Branchiobdella — noun type genus of the Branchiobdellidae: a small worm that lives on the gills or surface of a crayfish attached by a sucker • Syn: ↑Branchiobdella • Hypernyms: ↑worm genus • Member Holonyms: ↑Branchiobdellidae, ↑family Branchiobdellidae …   Useful english dictionary

  • genus Lemna — noun minute aquatic herbs floating on or below the water surface of still water consisting of a leaflike frond or plant body and single root • Syn: ↑Lemna • Hypernyms: ↑monocot genus, ↑liliopsid genus • Member Holonyms: ↑Lemnaceae, ↑family… …   Useful english dictionary

  • genus Lycaena — noun type genus of the Lycaenidae; small slender butterflies with upper surface of wings usually metallic blue or green or copper • Syn: ↑Lycaena • Hypernyms: ↑arthropod genus • Member Holonyms: ↑Lycaenidae, ↑family Lycaenidae …   Useful english dictionary

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”