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arXiv · 1701.04479

On geometric formality of rationally elliitic manifolds in dimensions $6$ and $7$

Svjetlana Terzic
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Abstract

We discuss the question of geometric formality for rationally elliptic manifolds of dimension $6$ and $7$. We prove that a geometrically formal six-dimensional biquotient with $b_{2}=3$ has the real cohomology of a symmetric space. We also show that a rationally hyperbolic six-dimensional manifold with $b_2\leq 2$ and $b_3=0$ can not be geometrically formal. As it follows from their real homotopy classification, the seven-dimensional geometrically formal rationally elliptic manifolds have the real cohomology of symmetric spaces as well.

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Svjetlana Terzic. 2017-10-01. On geometric formality of rationally elliitic manifolds in dimensions $6$ and $7$. https://arxiv.org/abs/1701.04479

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