Topological Properties
The abelian group maps the complex plane into the fundamental parallelogram. That is, every point can be written as for integers m,n, with a point p in the fundamental parallelogram.
Since this mapping identifies opposite sides of the parallelogram as being the same, the fundamental parallelogram has the topology of a torus. Equivalently, one says that the quotient manifold is a torus.
Read more about this topic: Fundamental Pair Of Periods
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—John Locke (1632–1704)