Related papers: Primitive stable representations in higher rank se…

For a finite group $G$, let $\sigma(G)$ be the number of subgroups of $G$ and $\sigma_\iota(G)$ the number of isomorphism types of subgroups of $G$. Let $L=L_r(p^e)$ denote a simple group of Lie type, rank $r$, over a field of order $p^e$…

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

In this paper we obtain uniform positive lower bounds on stable commutator length in word-hyperbolic groups and certain groups acting on hyperbolic spaces (namely the mapping class group acting on the complex of curves, and an amalgamated…

We study character varieties arising as moduli of representations of an orientable surface group into a reductive group $G$. We first show that if $G/Z$ acts freely on the representation variety, then both the representation variety and the…

In this paper, we study the graph of homothety classes of stable free lattices in a two-dimensional representation over a local UFD. This generalizes a classical result of the case where the base ring is a discrete valuation ring due to…

In this article we introduce order preserving representations of fundamental groups of surfaces into Lie groups with bi-invariant orders. By relating order preserving representations to weakly maximal representations, introduced in…

Let $G$ be a finite primitive permutation group on a set $\Omega$ with nontrivial point stabilizer $G_{\alpha}$. We say that $G$ is extremely primitive if $G_{\alpha}$ acts primitively on each of its orbits in $\Omega \setminus \{\alpha\}$.…

We provide detailed calculations for the classification of representations of compact simple Lie groups with non-empty boundary in the orbit space, first announced in a previous paper [arXiv:2112.00513] by the same authors.

Using Lusztig's total positivity in split real Lie groups V. Fock and A. Goncharov have introduced spaces of positive (framed) representations. For general semisimple Lie groups a generalization of Lusztig's total positivity was recently…

We provide a complete classification of when the homeomorphism group of a stable surface, $\Sigma$, has the automatic continuity property: Any homomorphism from Homeo$(\Sigma)$ to a separable group is necessarily continuous. This result…

Associated to every group with a weak spherical Tits system of rank n+1 with an appropriate rank n subgroup, we construct a relative spectral sequence involving group homology of Levi subgroups of both groups. Using the fact that such Levi…

A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of…

We study embeddings of groups of Lie type $H$ in characteristic $p$ into exceptional algebraic groups $\mathbf G$ of the same characteristic. We exclude the case where $H$ is of type $\mathrm{PSL}_2$. A subgroup of $\mathbf G$ is \emph{Lie…

For groups of prime order, equivariant stable maps between equivariant representation spheres are investigated using the Borel cohomology Adams spectral sequence. Features of the equivariant stable homotopy category, such as stability and…

A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids…

Let $\Gamma_1$ and $\Gamma_2$ be two lattices of finite covolume in a semisimple Lie group $G$. We prove a spectral rigidity result for the representation spectra of the right regular representations $L^2(\Gamma_1 \backslash G)$ and…

Let $A$ be a simple C*-algebra of stable rank one and let $p$ and $q$ be two $\sigma$-compact open projections. It is proved that there is a continuous path of unitaries in ${\tilde A}$ which connects open sub-projections of $p$ which is…

We consider the category of presheaves of Gamma-spaces, or equivalently, of Gamma-objects in simplicial presheaves. Our main result is the construction of stable model structures on this category parametrised by local model structures on…

We study geometric properties of compact stable minimal surfaces with boundary in homogeneous 3-manifolds $X$ that can be expressed as a semidirect product of $\mathbb{R}^2$ with $\mathbb{R}$ endowed with a left invariant metric. For any…

We consider a convex solid cone $\mathcal{C}\subset\mathbb{R}^{n+1}$ with vertex at the origin and boundary $\partial\mathcal{C}$ smooth away from $0$. Our main result shows that a compact two-sided hypersurface $\Sigma$ immersed in…