We obtain new calculations of the top weight rational cohomology of the moduli spaces M2,
n, equivalently the rational homology of the tropical moduli spaces Δ 2, n, as a …

We show that a certain locus inside the moduli space $ M_g $ of hyperbolic surfaces, given
by surfaces with" sufficiently many" short geodesics, is a classifying space of the handlebody …

We construct, for all $ g\geq 2$ and $ n\geq 0$, a spectral sequence of rational $ S_n $-
representations which computes the $ S_n $-equivariant reduced rational cohomology of …

We study the compactly supported rational cohomology of configuration spaces of points on
wedges of spheres, equipped with natural actions of the symmetric group and the group …

The automorphism group $\operatorname {Aut}(F_n) $ of the free group $ F_n $ acts on a
space $ A_d (n) $ of Jacobi diagrams of degree d on n oriented arcs. We study the …

Working over a field $ k $ of characteristic zero, the category of analytic contravariant
functors on the category of finitely-generated free groups is shown to be equivalent to the …

We express the hairy graph complexes computing the rational homotopy groups of long
embeddings (modulo immersions) of R m in R n as 'decorated'graph complexes associated …

We express the rational cohomology of the unordered configuration space of a compact
oriented manifold as a representation of its mapping class group in terms of a weight …

We show that if H is a cocommutative Hopf algebra, then there is a natural action of A ut (F n)
on H⊗ n which induces an O ut (F n) action on a quotient H⊗ n. In the case when H= T (V) is …

In order to solve two problems in deformation theory, we establish natural structures of
homotopy Lie algebras and of homotopy associative algebras on tensor products of …