Classification and Characterization of rationally elliptic manifolds in low dimensions

2014/09/29 by Martin Herrmann, Herrmann, Martin
Mathematics · #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #math.AT #math.DG

paper · pdf · doi:10.48550/arxiv.1409.8036

23 pages; extended Section 2, revised Section 5 and several minor revisions

arxiv created 2015/04/09 · arxiv updated 2015/04/10

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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