TITLE: Errata for Getzler-Kapranov "Cyclic operads and Cyclic homology"
QUESTION [7 upvotes]: Do you know if anyone made an errata for the Getzler-Kapranov paper "Cyclic operads and Cyclic homology"? I was trying to read it, and I have found (at least I think I did) quite a few typos not all of which are obvious. I have looked at the published version of this paper in the "Geometry, topology, & physics" but seems to be exactly the same as the preprint.
This paper has a lot of citations, so I thought it might be reasonable to ask.
Thank you very much!

REPLY [9 votes]: I am using this version of the paper, and it seems like the published version looks exactly like that. Here is what I have found.

First, a warning: Getzler and Kapranov use the term "quadratic operad" for what Loday-Vallette call "binary quadratic".
In example 4.5 (a), there is one more relation missing. Namely, we also need to include $B(x_1x_0,x_2)=B(x_0,x_2x_1)$ corresponding to the transposition $\sigma\in k[S_2]=Ass(2)$.
In the beginning of section 4.7, on page 17, the map called $B_n$ should come from the action of $\mathcal{P}$ on $A$.
In proposition 4.9, $A$ is the free $\mathcal{P}$-algebra $F(\mathcal{P},V)$ on $V$.
In the second formula in the proof of proposition 4.9, one should swap $p$ and $q$.
In the beginning of section 5.8, $\mathcal{Z}$ not necessarily a cyclic cooperad, can also be anti-cyclic, because the construction applies to the bar construction $\mathcal{BP}$, which is anti-cyclic.
In lemma 5.11(2) instead of the first $CA(\Phi,A)$ should be $CB$.
In lemma 5.12 in the RHS of the formula, $A$ should be replaced by $V$.
In section 6.6, there is a formula $CC_n(\Phi,A)\simeq CHarr_{n+1}(A,A)$, which in the diagram of section 6.9 becomes $CC_n(\Phi,A)\simeq CHarr_{n-1}(A,A)$. I think the first one is correct, but I am not sure here.
In the definition of $\lambda(\mathcal{Z},C)$ in section 6.11 on p.28, I think the map should be modified to be $C\otimes C\to \mathcal{Z}(n)\otimes C^{\otimes (n+1)}\to \mathcal{Z}(n)\otimes C^{\otimes (n+1)}$, where the last map is $1-\sigma$, for every $\sigma\in S_{n+1}$. Otherwise, the definition of Getzler-Kapranov for cooperads does not give a result dual to the usual definition for operads.

If you have found some more, please, add to this list! There are still plenty of places where I don't know what is going on.