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 [Wa3], which gives lower bounds of the dimensions of π k (BDiff(D 4 , ∂)) ⊗ Q in terms of the dimensions of Kontsevich's graph homology, and explain why it can be extended to arbitrary even dimensions d ≥ 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.). This has the structure of a manifold with corners induced from C r (R d ). § This sequence of blow-ups is different from the analogue of the successive blow-ups given in [FM, AS] in their derivation of the definition from (2.4). The sequence of blow-ups along (2.5) will be convenient for our purpose.¶ In [Si], Cn(X), C * r (V ), S A are denoted like Cn[X], Cr(V ), C T (X), respectively.

Corrigendum: On Kontsevich's characteristic classes for higher‐dimensional sphere bundles II: Higher classes

“…When ∞ ∈ 𝐴, let Γ 𝐴 be Γ∕𝐴 𝑐 , where 𝐴 𝑐 = {1, … , 𝑛} − 𝐴'. We refer the reader to [6] for more detail.…”