相关论文: Magnus subgroups of one-relator surface groups

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a…

We introduce the notion of splitting subgroups of quasireducitve supergroups, and explain their significance. For $GL(m|n)$, $Q(n)$, and defect one basic classical supergroups, we give explicit splitting subgroups. We further prove they are…

For infinite reductive groups with Frobenius maps, we show that certain subquotients of abstract representations of the groups induced from 1-dimensional representations of Borel subgroups are irreducible.

We establish that, given $\Sigma$ a compact orientable surface, and $G$ a finitely presented one-ended group, the set of copies of $G$ in the mapping class group $\mathcal{MCG}(\Sigma)$ consisting of only pseudo-anosov elements except…

In order to diagnose the cause of some defects in the category of canonical hypergroups, we investigate several categories of hyperstructures that generalize hypergroups. By allowing hyperoperations with possibly empty products, one obtains…

We define (in two, equivalent ways) the notion of a rigid stratum of a reductive group. This generalizes the notion of rigid unipotent class.

Let X be a smooth complex projective surface. We prove that for any sufficiently big m there exists a rational dominant map f from X into a complex rational ruled surface Y, such that f is generically finite of degree m and has monodromy…

We consider an arbitrary topological group $G$ definable in a structure $\mathcal M$, such that some basis for the topology of $G$ consists of sets definable in $\mathcal M$. To each such group $G$ we associate a compact $G$-space of…

Let H be a group obtained from a group G by adding one generator and one relator which is a proper power of a unimodular word. The main aim of this paper is to prove that G is a malnormal subgroup of H. This implies that if G is a…

We study algebraic structures of certain submonoids of the monoid of homology cylinders over a surface and the homology cobordism groups, using Reidemeister torsion with non-commutative coefficients. The submonoids consist of ones whose…

We characterize convex cocompact subgroups of the mapping class group of a surface in terms of uniform convergence actions on the zero locus of the limit set. We also construct subgroups that act as uniform convergence groups on their limit…

A very interesting problem in the classical theory of minimal surfaces consists of the classification of such surfaces under some geometrical and topological constraints. In this short paper, we give a brief summary of the known…

A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they…

Let $M(N_{h,n})$ denote the mapping class group of a compact nonorientable surface of genus $h\ge 7$ and $n\le 1$ boundary components, and let $T(N_{h,n})$ be the subgroup of $M(N_{h,n})$ generated by all Dehn twists. It is known that…

In this technical report we describe a general class of monoids for which (sub)sequential rational can be characterised in terms of a congruence relation in the flavour of Myhill-Nerode relation. The class of monoids that we consider can be…

We prove the congruence subgroup property for the centralizer of a finite subgroup $G$ in the mapping class group of a hyperbolic oriented and connected surface of finite topological type $S$ such that the genus of the quotient surface…

We show that a surface group contained in a reductive real algebraic group can be deformed to become Zariski dense, unless its Zariski closure acts transitively on a Hermitian symmetric space of tube type. This is a kind of converse to a…

In this note we study the finite groups whose subgroup lattices are dismantlable.

We prove that one-relator groups with torsion are hereditarily conjugacy separable. Our argument is based on a combination of recent results of Dani Wise and the first author. As a corollary we obtain that any quasiconvex subgroup of a…

The SU(2) TQFT representation of the mapping class group of a closed surface of genus g, at a root of unity of prime order, is shown to be irreducible. Some examples of reducible representations are also given.