Classification and characterization of rationally elliptic manifolds in low dimensions

Classification and characterization of rationally elliptic manifolds in low dimensions

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-ma...

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Veröffentlicht in:Mathematische Zeitschrift 2018-04, Vol.288 (3-4), p.1081-1101
1. Verfasser: Herrmann, Martin
Format: Artikel
Sprache:eng
Schlagworte:
Classification
Manifolds
Mathematics
Mathematics and Statistics
Rings (mathematics)
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Beschreibung
Zusammenfassung: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.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-017-1927-7