Geodesic
Resolutions of moduli spaces and homological stability
Journal of the European Mathematical Society, Tome 18 (2016) no. 1, pp. 1-81

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DOI

We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and gives explicit stability ranges in many new cases. In each of these cases the stable homology can be identified using the methods of Galatius, Madsen, Tillmann and Weiss.
DOI : 10.4171/jems/583
Classification : 55-XX, 20-XX, 57-XX
Keywords: Homological stability, mapping class groups, moduli spaces 
Oscar Randal-Williams. Resolutions of moduli spaces and homological stability. Journal of the European Mathematical Society, Tome 18 (2016) no. 1, pp. 1-81. doi: 10.4171/jems/583
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     title = {Resolutions of moduli spaces and homological stability},
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     doi = {10.4171/jems/583},
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