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 Dennis Sullivan (1977) and Daniel Quillen (1969).
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 (Félix, Halperin & Thomas 2001).
Read more about Rational Homotopy Theory: Rational Spaces, Sullivan Algebras, The Sullivan Minimal Model of A Topological Space, Formal Spaces, Examples, External Links
Famous quotes containing the words rational and/or theory:
“No actual skeptic, so far as I know, has claimed to disbelieve in an objective world. Skepticism is not a denial of belief, but rather a denial of rational grounds for belief.”
—William Pepperell Montague (1842–1910)
“Everything to which we concede existence is a posit from the standpoint of a description of the theory-building process, and simultaneously real from the standpoint of the theory that is being built. Nor let us look down on the standpoint of the theory as make-believe; for we can never do better than occupy the standpoint of some theory or other, the best we can muster at the time.”
—Willard Van Orman Quine (b. 1908)