Rational homotopy theory for non-simply connected spaces

Gómez-Tato, Antonio; Halperin, Stephen; Tanré, Daniel

doi:10.1090/S0002-9947-99-02463-0

Rational homotopy theory for non-simply connected spaces
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by Antonio Gómez-Tato, Stephen Halperin and Daniel Tanré PDF

Trans. Amer. Math. Soc. 352 (2000), 1493-1525 Request permission

Abstract:

We construct an algebraic rational homotopy theory for all connected CW spaces (with arbitrary fundamental group) whose universal cover is rationally of finite type. This construction extends the classical theory in the simply connected case and has two basic properties: (1) it induces a natural equivalence of the corresponding homotopy category to the homotopy category of spaces whose universal cover is rational and of finite type and (2) in the algebraic category, homotopy equivalences are isomorphisms. This algebraisation introduces a new homotopy invariant: a rational vector bundle with a distinguished class of linear connections.

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