Rational Spaces
A rational space is a simply connected space all of whose homotopy groups are vector spaces over the rational numbers. If X is any simply connected CW complex, then there is a rational space Y, unique up to homotopy equivalence, and a map from X to Y inducing an isomorphism on homotopy groups tensored with the rational numbers. The space Y is called the rationalization of X, and is the localization of X at the rationals, and is the rational homotopy type of X. Informally, it is obtained from X by killing all torsion in the homotopy groups of X.
Read more about this topic: Rational Homotopy Theory
Famous quotes containing the words rational and/or spaces:
“...if we would be and do all that as a rational being we should desire, we must resolve to govern ourselves; we must seek diversity of interests; dread to be without an object and without mental occupation; and try to balance work for the body and work for the mind.”
—Ellen Henrietta Swallow Richards (1842–1911)
“through the spaces of the dark
Midnight shakes the memory
As a madman shakes a dead geranium.”
—T.S. (Thomas Stearns)