In mathematics, a genus g surface (also known as a g-torus or g-holed torus) is a surface formed by the connected sum of g distinct tori: the interior of a disk is removed from each of g distinct tori and the boundaries of the g many disks are identified (glued together), forming a g-torus.
The genus of a connected orientable surface is an integer representing the maximum number of cuttings along non-intersecting closed simple curves without rendering the resultant manifold disconnected.
[2] Elliptic curves over the complex numbers can be identified with genus 1 surfaces.
[3] The term double torus is occasionally used to denote a genus 2 surface.
[6] The term triple torus is also occasionally used to denote a genus 3 surface.