On the non-realizability of braid groups by diffeomorphisms

Abstract For every compact surface $S$ of finite type (possibly with boundary components but without punctures), we show that when $n$ is sufficiently large there is no lift $\sigma $ of the surface braid group $B_n(S)$ to $ {\rm Diff}(S,n)$, the group of diffeomorphisms preserving $n$ marked points and restricting to the identity on the boundary. Our methods are applied to give a new proof of Morita's non-lifting theorem in the best possible range. These techniques extend to the more general setting of spaces of codimension-2 embeddings, and we obtain corresponding results for spherical motion groups, including the string motion group.