Mathematische Zeitschrift

, Volume 288, Issue 3–4, pp 1081–1101 | Cite as

Classification and characterization of rationally elliptic manifolds in low dimensions

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Abstract

We give a characterization of closed, simply connected, rationally elliptic 6-manifolds in terms of their rational cohomology rings and a partial classification of their real cohomology rings. We classify rational, real and complex homotopy types of closed, simply connected, rationally elliptic 7-manifolds. We give partial results in dimensions 8 and 9.

Keywords

Rationally elliptic spaces Rationally elliptic manifolds Minimal models Cohomology ring 

Mathematics Subject Classification

Primary 55P62 Secondary 57R19 

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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Fakultät für MathematikKarlsruher Institut für TechnologieKarlsruheGermany

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