# Genus-two surface

In mathematics, a **genus-two 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

## ExampleEdit

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

## See alsoEdit

## ReferencesEdit

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