Journal of the European Mathematical Society
Full-Text PDF (565 KB) | Metadata | Table of Contents | JEMS summary
Published online: 2015-12-16
Resolutions of moduli spaces and homological stabilityOscar Randal-Williams (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