Related papers: Residual $p$ properties of mapping class groups an…

Let G be a connected reductive group over an algebraically closed field of characteristic p. In an earlier paper we defined a surjective map \Phi_p from the set \underline{W} of conjugacy classes in the Weyl group W to the set of unipotent…

Let $M$ and $N$ be topological spaces, let $G$ be a group, and let $\tau \colon\thinspace G \times M \to M$ be a proper free action of $G$. In this paper, we define a Borsuk-Ulam-type property for homotopy classes of maps from $M$ to $N$…

We use the theory of group actions on profinite trees to prove that the fundamental group of a finite, 1-acylindrical graph of free groups with finitely generated edge groups is conjugacy separable. This has several applications: we prove…

Let $\Sigma_{g,p}$ be a closed oriented surface of genus $g\geq 1$ with $p$ punctures. Let $\rm Mod(\Sigma_{\textit{g,p}})$ be the mapping class group of $\Sigma_{g,p}$. Wajnryb proved in [Wa] that for $p=0, 1$ $\rm…

In this paper we define a $\mathbf{QP}^1$-valued class function on the mapping class group $\mathcal{M}_{g,2}$ of a surface $\Sigma_{g,2}$ of genus $g$ with two boundary components. Let $E$ be a $\Sigma_{g,2}$ bundle over a pair of pants…

Let $\Sigma_{g,n}$ be an orientable surface of genus $g$ with $n$ punctures. We study actions of the mapping class group of $\Sigma_{g,n}$ via Hodge-theoretic and arithmetic techniques. We show that if $$\rho: \pi_1(\Sigma_{g,n})\to…

Let $\textrm{Mod}(N_{g, p})$ denote the mapping class group of a nonorientable surface of genus $g$ with $p$ punctures. For $g\geq14$, we show that $\textrm{Mod}(N_{g, p})$ can be generated by five elements or by six involutions.

For any surface $\Sigma$ of infinite topological type, we study the Torelli subgroup ${\mathcal I}(\Sigma)$ of the mapping class group ${\rm MCG}(\Sigma)$, whose elements are those mapping classes that act trivially on the homology of…

We present a new short proof of the explicit formula for the group of links (and also link maps) in the 'quadruple point free' dimension. Denote by $L^m_{p,q}$ (respectively, $C^{m-p}_p$) the group of smooth embeddings $S^p\sqcup S^q\to…

Let $PB_n(S_{g,p})$ be the pure braid group of a genus $g>1$ surface with $p$ punctures. In this paper we prove that any surjective homomorphism $PB_n(S_{g,p})\to PB_m(S_{g,p})$ factors through one of the forgetful homomorphisms. We then…

We study probability measure preserving (p.m.p.) non-free actions of free groups and the associated IRS's. The perfect kernel of a countable group Gamma is the largest closed subspace of the space of subgroups of Gamma without isolated…

A locally compact group $G$ has property PL if every isometric $G$-action either has bounded orbits or is (metrically) proper. For $p>1$, say that $G$ has property $BP_{L^p}$ if the same alternative holds for the smaller class of affine…

We consider group measure space II$_1$ factors $M=L^{\infty}(X)\rtimes\Gamma$ arising from Bernoulli actions of ICC property (T) groups $\Gamma$ (more generally, of groups $\Gamma$ containing an infinite normal subgroup with relative…

We give completely combinatorial proofs of the main results of [3] using polygons. Namely, we prove that the mapping class group of a surface with boundary acts faithfully on a finitely-generated linear category. Along the way we prove some…

We show that $\delta$-separated branches of hyperbolic groups have the so-called $\Lambda_p$ property.

We continue our study of group algebras acting on $L^p$-spaces, particularly of algebras of $p$-pseudofunctions of locally compact groups. We focus on the functoriality properties of these objects. We show that $p$-pseudofunctions are…

Magnus proved that, given two elements $x$ and $y$ of a finitely generated free group $F$ with equal normal closures $\langle x\rangle^F=\langle y\rangle^F$, then $x$ is conjugated either to $y$ or $y^{-1}$. More recently, this property,…

In this paper we study conjugacy separability of subdirect products of two free (or hyperbolic) groups. We establish necessary and sufficient criteria and apply them to fibre products to produce a finitely presented group $G_1$ in which all…

Let $S$ be a closed oriented surface and $G$ a finite group of orientation preserving automorphisms of $S$ whose orbit space has genus at least $2$. There is a natural group homomorphism from the $G$-centralizer in $Diff^+(S)$ to the…

We study the action of the mapping class group M(F) on the complex of curves of a non-orientable surface F. We obtain, by using a result of K. S. Brown, a presentation for M(F) defined in terms of the mapping class groups of the…