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)
“Le silence éternel de ces espaces infinis m’effraie. The eternal silence of these infinite spaces frightens me.”
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