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