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.