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Transactions of the American Mathematical Society

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Rational homotopy theory
for non-simply connected spaces


Authors: Antonio Gómez-Tato, Stephen Halperin and Daniel Tanré
Journal: Trans. Amer. Math. Soc. 352 (2000), 1493-1525
MSC (1991): Primary 55P62, 55R25
DOI: https://doi.org/10.1090/S0002-9947-99-02463-0
Published electronically: November 18, 1999
MathSciNet review: 1653355
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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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Additional Information

Antonio Gómez-Tato
Affiliation: Departamento de Xeometría e Topoloxía, Universidade de Santiago de Compostela, Santiago de Compostela, 15706 España
Email: agtato@zmat.usc.es

Stephen Halperin
Affiliation: College of Computer, Mathematical and Physical Science, University of Maryland, College Park, Maryland 20742-3281
Email: shalper@deans.umd.edu

Daniel Tanré
Affiliation: U.R.A. CNRS 0751, U.F.R. de Mathématiques, Université des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq Cedex, France
Email: Daniel.Tanre@agat.univ-lille1.fr

DOI: https://doi.org/10.1090/S0002-9947-99-02463-0
Keywords: Fundamental group, simplicial set, Sullivan model, rational homotopy, rational vector bundle, linear connections
Received by editor(s): November 20, 1997
Published electronically: November 18, 1999
Additional Notes: The first author’s research was partially supported by an “Action Intégrée” and a Xunta of Galicia grant, the second author’s research was partially supported by a NATO grant and a NSERC grant and the third author’s research was partially supported by a NATO grant.
Article copyright: © Copyright 2000 American Mathematical Society

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