Journal of the European Mathematical Society


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Volume 18, Issue 1, 2016, pp. 1–81
DOI: 10.4171/JEMS/583

Published online: 2015-12-16

Resolutions of moduli spaces and homological stability

Oscar Randal-Williams[1]

(1) University of Cambridge, UK

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.

Keywords: Homological stability, mapping class groups, moduli spaces

Randal-Williams Oscar: Resolutions of moduli spaces and homological stability. J. Eur. Math. Soc. 18 (2016), 1-81. doi: 10.4171/JEMS/583