Solid torus

In mathematics, a solid torus is the topological space formed by sweeping a disk around a circle. It is homeomorphic to the Cartesian product of the disk and the circle, endowed with the product topology. A standard way to visualize a solid torus is as a toroid, embedded in 3-space. However, it should be distinguished from a torus, which has the same visual appearance: the torus is the two-dimensional space on the boundary of a toroid, while the solid torus includes also the compact interior space enclosed by the torus.

The solid torus is a connected, compact, orientable 3-dimensional manifold with boundary. The boundary is homeomorphic to , the ordinary torus.

Since the disk is contractible, the solid torus has the homotopy type of a circle, . Therefore the fundamental group and homology groups are isomorphic to those of the circle:


This page was last edited on 24 November 2017, at 19:40 (UTC).
Reference: https://en.wikipedia.org/wiki/Solid_tori under CC BY-SA license.

Related Topics


Warning: DOMDocument::loadHTML(): Tag math invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag semantics invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mstyle invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag msup invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mn invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mo invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag msup invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mn invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag annotation invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag math invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag semantics invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mstyle invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag msup invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mn invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mo invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag msup invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mn invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag annotation invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag math invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag semantics invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mstyle invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag msup invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mn invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag annotation invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag math invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag semantics invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mstyle invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag msup invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mn invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag annotation invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Recently Viewed