- Genus-2 surface
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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
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
- Weisstein, Eric W., "Double Torus" from MathWorld.
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