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:
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—Ralph Waldo Emerson (1803–1882)
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—Blaise Pascal (1623–1662)