Classification and Characterization of rationally elliptic manifolds in low dimensions

TL;DR

This paper classifies and characterizes low-dimensional rationally elliptic manifolds, focusing on their cohomology rings and homotopy types in dimensions 6 to 9.

Contribution

It provides a detailed characterization of 6-manifolds and classifies homotopy types of 7-manifolds, advancing understanding of rational ellipticity in low dimensions.

Findings

Characterization of 6-manifolds via rational cohomology rings

Classification of 7-manifolds' homotopy types

Partial results for dimensions 8 and 9

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.