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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.

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  1. Fakultät für Mathematik, Karlsruher Institut für Technologie, Kaiserstrasse 89-93, 76133, Karlsruhe, Germany

    Martin Herrmann

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  1. Martin Herrmann
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Correspondence to Martin Herrmann.

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Herrmann, M. Classification and characterization of rationally elliptic manifolds in low dimensions. Math. Z. 288, 1081–1101 (2018). https://doi.org/10.1007/s00209-017-1927-7

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  • DOI: https://doi.org/10.1007/s00209-017-1927-7

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