Related papers: A Fixed Point Theorem for Deformation Spaces of G-…

Baumslag conjectured in the 1970s that the automorphism tower of a finitely generated free nilpotent group must be very short. Let F_{n,c} denote a free nilpotent group of finite rank n at least two and of nilpotency class c at least two.…

We associate a contractible ``outer space'' to any free product of groups G=G_1*...*G_q. It equals Culler-Vogtmann space when G is free, McCullough-Miller space when no G_i is Z. Our proof of contractibility (given when G is not free) is…

Let $\sigma$ denote an endomorphism of a smooth algebraic group $G$ over the algebraic closure of a finite field, and assume all iterates of $\sigma$ have finitely many fixed points. Steinberg gave a formula for the number of fixed points…

We establish a fixed-point theorem for the face maps that consist in deleting the $i$th entry of an ordered set. Furthermore, we show that there exists random finite sets of integers that are almost invariant under such deletions.…

We show that for singular hypersurfaces, a version of their genus-zero Gromov-Witten theory may be described in terms of a direct limit of fixed point Floer cohomology groups, a construction which is more amenable to computation and easier…

Let $G$ be a (compact) special group in the sense of Haglund and Wise. We show that ${\rm Out}(G)$ is finitely generated, and provide a virtual generating set consisting of Dehn twists and ``pseudo-twists''. We exhibit instances where Dehn…

We give a short and elementary proof of the non-realizability of the mapping class group via homeomorphisms. This was originally established by Markovic, resolving a conjecture of Thurston. With the tools established in this paper, we also…

When 1 -> H -> G -> Q -> 1 is a short exact sequence of three infinite, word-hyperbolic groups, Mahan Mitra (Mj) has shown that the inclusion map from H to G extends continuously to a map between the Gromov boundaries of H and G. This…

Any finite group can be encoded as the automorphism group of an unlabeled simple graph. Recently Hartke, Kolb, Nishikawa, and Stolee (2010) demonstrated a construction that allows any ordered pair of finite groups to be represented as the…

Given a group retraction $r: G \rightarrow H $, we construct a finite topological space $ X_r $ of height 1, together with a topological retraction $\overline{r}: X_r \rightarrow X_r $, such that the group of automorphisms $…

We show that many countable groups acting on trees, including free products of infinite countable groups and surface groups, are isomorphic to dense subgroups of isometry groups of bounded Urysohn spaces. This extends previous results of…

We show that any twisted Dijkgraaf-Witten representation of a mapping class group of an orientable, compact surface with boundary has finite image. This generalizes work of Etingof, Rowell and Witherspoon showing that the braid group images…

We consider the action of a finite subgroup of the mapping class group $Mod(S)$ of an oriented compact surface $S$ of genus $g \geq 2$ on the moduli space $\mathcal{R}(S,G)$ of representations of $\pi_1(S)$ in a connected semisimple real…

It is shown that for any action of a finitely presented group $G$ on an $\R$-tree, there is a decomposition of $G$ as the fundamental group of a graph of groups related to this action. If the action of $G$ on $T$ is non-trivial, i.e. there…

Let $\mathcal G$ denote the space of finitely generated marked groups. For any finitely generated group $G$, we construct a continuous, injective map $f$ from the space of subgroups $Sub(G)$ to $\mathcal G$ that sends conjugate subgroups to…

For $S=S_{g,n}$ a closed orientable differentiable surface of genus $g$ from which $n$ points have been removed, such that $\chi(S)=2-2g-n<0$, let $\mathrm{P}\Gamma(S)$ be the pure mapping class group of $S$ and…

Hughes has defined a class of groups, which we call FSS (finite similarity structure) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-known example is Thompson's group V. Guided by previous work on…

Let $S$ be a surface of finite type which is not a sphere with at most four punctures, a torus with at most two punctures, or a closed surface of genus two. Let $\mathcal{MF}$ be the space of equivalence classes of measured foliations of…

Let $(S,\, \ast)$ be a closed oriented surface with a marked point, let $G$ be a fixed group, and let $\rho\colon\pi_1(S) \longrightarrow G$ be a representation such that the orbit of $\rho$ under the action of the mapping class group…

We describe the action of the mapping class group $M(g,n)$ on the fundamental group of $T_{g,n}$, a compact orientable topological surface of positive genus $g$ with $n$ marked points. This is achieved by computing the image of the…