Addendum to: Some exotic nontrivial elements of the rational homotopy groups of $\mathrm{Diff}(S^4)$ (homological interpretation)

Abstract

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 ${\pi }_k(B\mathrm{Diff}(D^4,\partial ))\otimes \mathbb{Q}$ in terms of the dimensions of Kontsevich's graph homology, and explain why it can be extended to arbitrary even dimensions $d\ge 4$. 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.

arXiv comment112 pages, 52 figures. v3: updated references, corrected mistakes, added Appendix C, D. Page rotation at p.14 in the pdf file is caused by ps2pdf. (ps file is correctly generated.) A correctly typeset pdf file can be downloaded from the author's website (https://www.math.kyoto-u.ac.jp/~tadayuki.watanabe/). Or please convert from the ps file by "ps2pdf -dAutoRotatePages=/None (filename).ps"

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