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

TL;DR

This paper provides a differential form interpretation of a previous proof related to the rational homotopy groups of the diffeomorphism group of 4-spheres, extending the results to higher even dimensions and making the proof more accessible.

Contribution

It introduces a differential form perspective on the main theorem of arXiv:1812.02448 and explains its extension to all even dimensions d ≥ 4, without requiring advanced background knowledge.

Findings

Lower bounds on the dimensions of rational homotopy groups of Diff(D^4,∂)

Extension of the proof to arbitrary even dimensions ≥ 4

Accessibility improvements for the proof's presentation

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 $d\geq 4$. 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.