Erratum: Braided Thompson's groups are of type F_∞ (J. reine angew. Math. 718 (2016) (59-101) DOI: 10.1515/crelle-2014-0030)

There is a mistake in Lemma 3.9 of [1], which has no consequences for the rest of the article. The assumption that the link of every k-simplex in X be m2k-2/-connected is insufficient to get the induction step to work, and needs to be replaced by m-k-2/-connected. The correct statement therefore reads: Lemma 3.9 (Reduction to the simplexwise injective case). LetY be a compactm-dimensional combinatorial manifold. Let X be a simplicial complex and assume that the link of every k-simplex in X is m k2-connected. Let W Y X be a simplicial map whose restriction to Y is simplexwise injective. Then after possibly subdividing the simplicial structure of Y is homotopic relative àY to a simplexwise injective map. We became aware of this mistake through discussions with Søren Galatius involving an equivalent result with the correct bound [2, Theorem 2.4]. In the new formulation the old proof applies verbatim, but we extend the presentation to confirm that the induction step, which breaks down when using the old bound, now works.