surface

A surface is a two-dimensional topological manifold. 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 sum operation, they make available a powerful language to be explored and exploited.

As an example of a surface take $T=S^1\times S^1$ the two torus, the boundary of a solid sugar donut shaped cake $D^2\times S^1$, where $S^1$ 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