Formality on rationalizations of simply connected CW complexes

Jingwen Gao; Xiugui Liu

Formality on rationalizations of simply connected CW complexes

Algebraic Topology 2021-05-13 v2

Authors: Jingwen Gao , Xiugui Liu

Abstract

In this paper, we show that for a simply connected CW complex $Y$ with $H^{*}(Y;\mathbb{Q})$ of finite dimension, if $H^{*}(Y;\mathbb{Q})$ is concentrated in degrees $\leq 3$ , then the rationalization $Y_\mathbb{Q}$ is formal. As an application, we show that the spatial realizations of simply connected Sullivan algebras with rational homology concentrated in degrees $\leq 3$ are formal.

Cite

@article{arxiv.2105.04751,
  title  = {Formality on rationalizations of simply connected CW complexes},
  author = {Jingwen Gao and Xiugui Liu},
  journal= {arXiv preprint arXiv:2105.04751},
  year   = {2021}
}

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