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In mathematics, rational homotopy theory is the study of the rational homotopy type of a space, which means roughly that one ignores all torsion in the homotopy groups. It was started by and . Rational homotopy types of simply connected spaces can be identified with (isomorphism classes of) certain algebraic objects called minimal Sullivan algebras, which are commutative differential graded algebras over the rational numbers satisfying certain conditions. The standard textbook on rational homotopy theory is . ==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''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Rational homotopy theory」の詳細全文を読む スポンサード リンク
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