Manifolds and cobordisms
The torus is the manifold obtained as the quotient
of the Cartesian plane, regarded as an abelian group, by the subgroup of pairs of integers.
More generally, for any natural number, the -torus is
For this is the circle.
In this fashion each torus canonically carries the structure of an abelian group, in fact of an abelian Lie group
Revised on November 7, 2013 10:44:11
by Urs Schreiber