附录：$\mathrm{Diff}(S^4)$的有理同伦群的一些奇异非平凡元素（同调解释）
Addendum to: Some exotic nontrivial elements of the rational homotopy groups of $\mathrm{Diff}(S^4)$ (homological interpretation)
摘要：
在本附录中，我们给出了arXiv：1812.02448的主要定理证明的微分形式解释，该定理给出了$π_k(B\mathrm{Diff}(D^4,\partial))\otimes\mathbb{Q}$的维数的下界，并解释了为什么它可以扩展到任意偶数维$d\geq 4$。我们试图使更多的读者能理解校样。因此，我们不假设熟悉位形空间积分，也不假设熟悉有限型不变量。本附录的一部分可能会加入原始文章时，将重新提交给杂志。这不是为了纠正以前的版本。
英文摘要：
In this addendum, we give a differential form interpretation of the proof of the main theorem of arXiv:1812.02448, which gives lower bounds of the dimensions of $π_k(B\mathrm{Diff}(D^4,\partial))\otimes\mathbb{Q}$ in terms of the dimensions of Kontsevich's graph homology, and explain why it can be extended to arbitrary even dimensions $d\geq 4$. We attempted to make the proof accessible to more readers. Thus we do not assume familiarity with configuration space integrals nor knowledge of finite type invariants. Part of this addendum might be joined to the original article when it will be re-submitted to the journal. This is not aimed at giving a correction to the previous version.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
