A surface is a two-dimensional topological manifoldMathworldPlanetmathPlanetmath. A closed surface is a surface without boundary.

A result called the “classification theorem” gives us a symbolic semantics, matching the geometrical view point, in terms of genera, orientability and number of boundary components. Together with the connected sumMathworldPlanetmathPlanetmath operation, they make available a powerful language to be explored and exploited.

As an example of a surface take T=S1×S1 the two torus, the boundary of a solid sugar donut shaped cake D2×S1, where S1 is the familiar modulus one complex numbers.

Title surface
Canonical name Surface
Date of creation 2013-03-22 16:01:43
Last modified on 2013-03-22 16:01:43
Owner juanman (12619)
Last modified by juanman (12619)
Numerical id 13
Author juanman (12619)
Entry type Definition
Classification msc 57M20
Related topic Manifold
Related topic NonOrientableSurface