English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Due to the deep work of Tillmann, Madsen, Weiss and Galatius, the cohomologyof the stable mapping class group $\gaminf$ is known with rational or finitefield coefficients. Little is known about the integral cohomology. In thispaper, we study the first four cohomology groups. Also, we compute the firstfew steps of the Postnikov tower of $B \gaminf^+$, the Quillen plusconstruction applied to $B \gaminf$. Our method relies on the Madsen-Weisstheorem, a few known computations of stable homotopy groups of spheres andprojective spaces and on a certain action of the binary icosahedral group on asurface. Using the latter, we can also describe an explicit geometric generatorof the third homotopy group $\pi_3 (B \gaminf)$.

The low-dimensional homotopy of the stable mapping class group