A 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.



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

See alsoEdit


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

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