Related papers: Commensurability of geometric subgroups of mapping…

We refine the construction of quasi-homomorphisms on mapping class groups. It is useful to know that there are unbounded quasi-homomorphisms which are bounded when restricted to particular subgroups since then one deduces that the mapping…

The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…

Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…

This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian…

The distributive property can be studied through bilinear maps and various morphisms between these maps. The adjoint-morphisms between bilinear maps establish a complete abelian category with projectives and admits a duality. Thus the…

We consider linear groups which do not contain unipotent elements of infinite order, which includes all linear groups in positive characteristic, and show that this class of groups has good properties which resemble those held by groups of…

To each projective hypersurface which is not a cone, we associate an abelian linear algebraic group called the symmetrizer group of the corresponding symmetric form. This group describes the set of homogeneous polynomials with the same…

For a metric space $X$ we study metrics on the two copies of $X$. We define composition of such metrics and show that the equivalence classes of metrics are a semigroup $M(X)$ Our main result is that $M(X)$ is an inverse semigroup,…

Let $G$ be a real Lie group with Lie algebra $\mathfrak g$. Given a unitary representation $\pi$ of $G$, one obtains by differentiation a representation $d\pi$ of $\mathfrak g$ by unbounded, skew-adjoint operators. Representations of…

This paper initiates a systematic study of the relation of commensurability of surface automorphisms, or equivalently, fibered commensurability of 3-manifolds fibering over the circle. We show that every hyperbolic fibered commensurability…

We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…

Admissible vectors for unitary representations of locally compact groups are the basis for group-frame and covariant coherent state expansions. Main tools in the study of admissible vectors have been Plancherel and central integral…

We classify the orientably regular maps which are elementary abelian regular branched coverings of Platonic maps M, in the case where the covering group and the rotation group G of M have coprime orders. The method involves studying the…

This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous…

A normal subgroup of the (extended) mapping class group of a surface is said to be geometric if its automorphism group is the mapping class group. We prove that in the case of the Cantor tree surface, every normal subgroup is geometric. We…

In this article, we prove that the commensurability class of a closed, orientable, hyperbolic 3-manifold is determined by the surface subgroups of its fundamental group. Moreover, we prove that there can be only finitely many closed,…

We determine the set of geometric endomorphism algebras of geometrically split abelian surfaces defined over $\mathbb{Q}$. In particular we find that this set has cardinality 92. The essential part of the classification consists in…

We focus on two kinds of infinite index subgroups of the mapping class group of a surface associated with a Lagrangian submodule of the first homology of a surface. These subgroups, called Lagrangian mapping class groups, are known to play…

We survey some recent developments at the interface of algebraic geometry, surface topology, and the theory of ordinary differential equations. Motivated by "non-abelian" analogues of standard conjectures on the cohomology of algebraic…

In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…