We construct a slant product $/ \colon \mathrm{S}_p(X \times Y) \mathrm{K}_{1-q}(\mathfrak{c}^{\mathrm{red}}Y) \to \mathrm{S}_{p-q}(X)$ on the analytic structure group of Higson and Roe K-theory stable corona Emerson Meyer. The latter is domain co-assembly map $\mu^\ast \mathrm{K}_{1-\ast}(\mathfrak{c}^{\mathrm{red}}Y) \mathrm{K}^\ast(Y)$. obtain such products entire Higson--Roe sequence. They ...

This paper answers a basic question about the Birman exact sequence in theory of mapping class groups. We prove that does not admit section over any subgroup $\Gamma$ contained Torelli group with finite index. A fortiori this proves there is no for finite-index full group. theorem was announced 1990 preprint G. Mess, but an error uncovered and described recent first author.