-stability and homomorphisms into the mapping class group
Marc Burger
ETH Zürich, SwitzerlandAlessandra Iozzi
ETH Zürich, Switzerland
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Abstract
We prove that any homomorphism into the mapping class group from a group satisfying a certain cohomological condition, called \textit{-stability}, is trivial. We show that such a condition is satisfied by all groups for which the above non-existence result was already known, hence providing in particular a unified proof in the above cases. We give moreover new examples of -stable groups.