# 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 |