The n-torus, denoted Tn, is a smooth orientable n dimensional manifold which is the product of n 1-spheres, i.e. Tn=S1××S1n.

Equivalently, the n-torus can be considered to be n modulo the action (vector addition) of the integer lattice n.

The n-torus is in addition a topological groupMathworldPlanetmath. If we think of S1 as the unit circle in and Tn=S1××S1n, then S1 is a topological group and so is Tn by coordinate-wise multiplication. That is,

Title n-torus
Canonical name Ntorus
Date of creation 2013-03-22 13:59:58
Last modified on 2013-03-22 13:59:58
Owner ack (3732)
Last modified by ack (3732)
Numerical id 7
Author ack (3732)
Entry type Definition
Classification msc 22C05
Classification msc 54B10
Related topic Torus