Related papers: Mapping Class Group Representations Derived from S…
In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form $n$ over a field $k$ of characteristic not two, and a category arising from an action…
In this paper, we construct and study derived character maps of finite-dimensional representations of $\infty$-groups. As models for $\infty$-groups we take homotopy simplicial groups, i.e. homotopy simplicial algebras over the algebraic…
It is proved that the mapping class group of any closed surface with finitely many marked points is quasiisometric to a CAT(0) cube complex. We provide two distinct proofs, one tailored to mapping class groups, and one applying to a larger…
We construct a boundary for the mapping class group Mod(S) of a surface S of finite type. The action of Mod(S) on this boundary is minimal, strongly proximal and topologically free. The boundary is the boundary of an EZ-structure for…
For an infinite dimensional Lie group $G$ modelled on a locally convex Lie algebra $\mathfrak{g}$, we prove that every smooth projective unitary representation of $G$ corresponds to a smooth linear unitary representation of a Lie group…
We show that if a Heegaard splitting is the result of stabilizing a high distance Heegaard splitting exactly once then its mapping class group is finitely generated.
We compute the invariant subspace of the rational group ring of a surface, truncated by powers of the augmentation ideal, under the action of the mapping class group. The surface is compact, oriented with one boundary component. This…
The stated skein algebra of a punctured bordered surface (or equivalently, a marked surface) is a generalization of the well-known Kauffman bracket skein algebra of unmarked surfaces and can be considered as an extension of the quantum…
We give a necessary and sufficient smoothness condition for the scheme parameterizing the n-dimensional representations of a finitely generated associative algebra over an algebraically closed field of characteristic zero. In particular,…
We show that the mapping class group acts properly on the space of maximal representations of the fundamental group of a closed Riemann surface into G when G = Sp(2n,R), SU(n,n), SO*(2n) or Spin(2,n).
The paper is concerned with `geometrization' of smooth (i.e. with open stabilizers) representations of the automorphism group of universal domains, and with the properties of `geometric' representations of such groups. As an application, we…
The aim of this paper is to study the virtual classes of representation varieties of surface groups onto the rank one affine group. We perform this calculation by three different approaches: the geometric method, based on stratifying the…
We use the representation theory of preprojective algebras to construct and study certain cluster algebras related to semisimple algebraic groups.
In this paper we introduce the framed pure braid group on $n$ strands of an oriented surface, a topological generalisation of the pure braid group $P_n$. We give different equivalents definitions for framed pure braid groups and we study…
We define vertex cover algebras for weighted simplicial multicomplexes and prove basics properties of them. Also, we describe these algebras for multicomplexes which have only one maximal facet and we prove that they are finitely generated.
In this paper the author finds explicitly all finite-dimensional irreducible representations of a series of finite permutation groups that are homomorphic images of Artin braid group.
We study the restriction to the symmetric group, $\mc{S}_n$ of the adjoint representation of $\mt{GL}_n(\C)$. We determine the irreducible constituents of the space of symmetric as well as the space of skew-symmetric $n\times n$ matrices as…
In this paper we give new presentations of the braid groups and the pure braid groups of a closed surface. We also give an algorithm to solve the word problem in these groups, using the given presentations.
To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over…
We study the large-scale geometry of mapping class groups of surfaces of infinite type, using the framework of Rosendal for coarse geometry of non locally compact groups. We give a complete classification of those surfaces whose mapping…