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Abstract Given a family of groups admitting a braided monoidal structure (satisfying mild assumptions) we construct a family of spaces on which the groups act and whose connectivity yields, via a… (More)

S. Galatius was partially supported by NSF grants DMS-1105058 and DMS-1405001, the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation pro- gramme (grant… (More)

We study the cohomology of Aut(F_n) and Out(F_n) with coefficients in the modules \wedge^q H, \wedge H^*, Sym^q H or Sym^q H^*, where H is the Out(F_n)-module obtained by abelianising the free group… (More)

We prove an analogue of the Madsen–Weiss theorem for high-dimensional manifolds. In particular, we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are… (More)

We prove new homological stability results for general linear groups over finite fields. These results are obtained by constructing CW approximations to the classifying spaces of these groups, in the… (More)

Combining results of Wahl, Galatius‐Madsen‐Tillmann‐Weiss and Korkmaz, one can identify the homotopy type of the classifying space of the stable nonorientable mapping class group N1 (after… (More)

We study the moduli spaces which classify smooth sur- faces along with a complex line bundle. There are homological sta- bility and Madsen-Weiss type results for these spaces (mostly due to Cohen and… (More)

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… (More)

We give a set of foundations for cellular $E_k$-algebras which are especially convenient for applications to homological stability. We provide conceptual and computational tools in this setting, such… (More)

We study the space of oriented genus g subsurfaces of a fixed manifold M, and in particular its homological properties. We construct a "scanning map" which compares this space to the space of… (More)