Double torus


Double torus

In mathematics, a double torus is a topological object formed by the connected sum of two torii. That is to say, from each of two torii 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" torii. A connected sum of torii 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 torii, or a connected sum of projective planes.

Double torus knots are studied in knot theory.

Example

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

References

* James R. Munkres, "Topology, Second Edition", Prentice-Hall, 2000, ISBN 0-13-181629-2.

* William S. Massey, "Algebraic Topology: An Introduction", Harbrace, 1967.


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Double torus knot — A double torus knot is a closed curve drawn on the surface called a double torus (think of the surface of two doughnuts stuck together). More technically, a double torus knot is the homeomorphic image of a circle in S³ which can be realized as a… …   Wikipedia

  • Torus (disambiguation) — Torus or tori may refer to:In mathematics:* Torus a surface * Torus knot * Algebraic torus * Double torus * Umbilic torusIn medicine:* Torus palatinus a bony growth on the palate * Torus mandibularis a bony growth on the mandible * Torus fracture …   Wikipedia

  • 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

  • Double Star mission — Double Star is a joint satellite based space mission by the China National Space Administration (CNSA) and the European Space Agency (ESA). It is the first space mission launched by China to investigate Earth s magnetosphere. It consists of two… …   Wikipedia

  • Double affine braid group — In mathematics, a double affine braid group is a group containing the braid group of an affine Weyl group. Their group rings have quotients called double affine Hecke algebras in the same way that the group rings of affine braid groups have… …   Wikipedia

  • Cycle double cover — Unsolved problems in mathematics Does every bridgeless graph have a multiset of cycles covering every edge exactly twice? …   Wikipedia

  • Möbius–Kantor graph — Named after August Ferdinand Möbius and S. Kantor Vertices 16 …   Wikipedia

  • 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… …   Wikipedia

  • List of knot theory topics — Knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician s knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical… …   Wikipedia

  • List of mathematics articles (D) — NOTOC D D distribution D module D D Agostino s K squared test D Alembert Euler condition D Alembert operator D Alembert s formula D Alembert s paradox D Alembert s principle Dagger category Dagger compact category Dagger symmetric monoidal… …   Wikipedia