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Free representations of outer automorphism groups of free products via characteristic abelian coverings

Given a free product 𝐺, we investigate the existence of faithful free representations of the outer automorphism group Out⁡(G)\operatorname{Out}(G), or in other words of embeddings of Out⁡(G)\operatorname{Out}(G) into Out⁡(Fm)\operatorname{Out}(F_{m}) for some 𝑚. This is based on work of Bridson and Vogtmann in which they construct embedding...