We study families of diffeomorphisms detected by trivalent graphs via the Kontsevich classes. We specify some recent results and constructions of the second named author to show that those non-trivial elements in homotopy groups $\text{◂f()▸}{\pi }_{\ast }\text{◂()▸}(B{\mathrm{Diff}}_{\partial }(D^d))\otimes \mathbb{Q}$ are lifted to homotopy groups of the moduli space of $h$-cobordisms $\text{◂f()▸}{\pi }_{\ast }\text{◂()▸}(B{\mathrm{Diff}}_{\bigsqcup }(D^d\times I))\otimes \mathbb{Q}$. As a geometrical application, we show that those elements in $\text{◂f()▸}{\pi }_{\ast }\text{◂()▸}(B{\mathrm{Diff}}_{\partial }(D^d))\otimes \mathbb{Q}$ for $d⩾4$ are also lifted to the rational homotopy groups $\text{◂f()▸}{\pi }_{\ast }\text{◂()▸}({\mathcal{M}}_{\partial }^{\mathsf{psc}}\text{◂◽.▸}{(D^d)}_{h_0})\otimes \mathbb{Q}$ of the moduli space of positive scalar curvature metrics. Moreover, we show that the same elements come from the homotopy groups $\text{◂f()▸}{\pi }_{\ast }\text{◂()▸}({\mathcal{M}}_{\bigsqcup }^{\mathsf{psc}}\text{◂◽.▸}{(D^d\times I;g_0)}_{h_0})\otimes \mathbb{Q}$ of moduli space of concordances of positive scalar curvature metrics on $D^d$ with fixed-round metric $h_0$ on the boundary $\text{◂◽˙▸}{S}^{d-1}$.

中文翻译：

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三价图检测到的微分同胚族和一致性

我们通过 Kontsevich 类研究由三价图检测到的微分同胚族。我们指定了第二位作者的一些最新结果和构造，以表明同伦群中的那些非平凡元素$\text{◂f()▸}{\pi }_{＊}\text{◂()▸}(乙{\mathrm{差异}}_{\partial }({丁}^d))\otimes \mathbb{问}$被提升到模空间的同伦群$H$-并列主义$\text{◂f()▸}{\pi }_{＊}\text{◂()▸}(乙{\mathrm{差异}}_{\bigsqcup }({丁}^d\times 我))\otimes \mathbb{问}$. 作为一个几何应用，我们展示了那些元素$\text{◂f()▸}{\pi }_{＊}\text{◂()▸}(乙{\mathrm{差异}}_{\partial }({丁}^d))\otimes \mathbb{问}$为了$d⩾\mathrm{4个}$也被提升到有理同伦群$\text{◂f()▸}{\pi }_{＊}\text{◂()▸}({\mathcal{米}}_{\partial }^{\mathsf{PSC}}\text{◂◽.▸}{({丁}^d)}_{H_0})\otimes \mathbb{问}$正标量曲率度量的模空间。此外，我们证明相同的元素来自同伦群$\text{◂f()▸}{\pi }_{＊}\text{◂()▸}({\mathcal{米}}_{\bigsqcup }^{\mathsf{PSC}}\text{◂◽.▸}{({丁}^d\times 我;G_0)}_{H_0})\otimes \mathbb{问}$正标量曲率度量的一致性模空间${丁}^d$固定圆公制$H_0$在边界上$\text{◂◽˙▸}{\mathrm{小号}}^{d-\mathrm{1个}}$.