$E_{2}$-cells and mapping class groups

Galatius, Søren; Kupers, Alexander; Randal-Williams, Oscar

doi:10.1007/s10240-019-00107-8

Geodesic

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Article

E_{2}

-cells and mapping class groups

Galatius, Søren ¹ ; Kupers, Alexander ¹ ; Randal-Williams, Oscar ¹

Publications Mathématiques de l'IHÉS, Tome 130 (2019), pp. 1-61

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Résumé

We prove a new kind of stabilisation result, “secondary homological stability,” for the homology of mapping class groups of orientable surfaces with one boundary component. These results are obtained by constructing CW approximations to the classifying spaces of these groups, in the category of $E_{2}$ -algebras, which have no $E_{2}$ -cells below a certain vanishing line.

DOI : 10.1007/s10240-019-00107-8

Affiliations des auteurs :

Galatius, Søren ¹ ; Kupers, Alexander ¹ ; Randal-Williams, Oscar ¹

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     title = {$E_{2}$-cells and mapping class groups},
     journal = {Publications Math\'ematiques de l'IH\'ES},
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     publisher = {Springer Berlin Heidelberg},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00107-8/}
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Galatius, Søren; Kupers, Alexander; Randal-Williams, Oscar. $E_{2}$-cells and mapping class groups. Publications Mathématiques de l'IHÉS, Tome 130 (2019), pp. 1-61. doi: 10.1007/s10240-019-00107-8

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