Related papers: Normal subgroups of big mapping class groups

Suppose that $X$ and $Y$ are surfaces of finite topological type, where $X$ has genus $g\geq 6$ and $Y$ has genus at most $2g-1$; in addition, suppose that $Y$ is not closed if it has genus $2g-1$. Our main result asserts that every…

For each compact almost Kahler manifold $(X,\om,J)$ and an element A of $H_2(X;Z)$, we describe a closed subspace $\ov{\frak M}_{1,k}^0(X,A;J)$ of the moduli space $\ov{\frak M}_{1,k}(X,A;J)$ of stable J-holomorphic genus-one maps such that…

We give conditions on the subgroups of the circle to be realized as the subgroups of eigenvalues of minimal Cantor systems belonging to a determined strong orbit equivalence class. Actually, the additive group of continuous eigenvalues…

Among compact Hausdorff groups G whose maximal profinite quotient is finitely generated, we characterize those that possess a proper dense normal subgroup. We also prove that the abstract commutator subgroup [H,G] is closed for every closed…

A completely simple semigroup S is a semigroup without zero which has no proper ideals and contains a primitive idempotent. It is known that S is a regular semigroup and any completely simple semigroup is isomorphic to the Rees matrix…

This paper is a continuation of our 2005 paper on complex topology and its implication on invertibility (or non-invertibility). In this paper, we will try to classify the complexity of inversion into 3 different classes. We will use…

If $K$ is a closed subgroup of a compact group $G$, the probability that randomly chosen pair of elements from $K$ and $G$ commute is denoted by $Pr(K,G)$. Say that a subgroup $K\leq G$ is $\epsilon$-central in $G$ if $Pr(\langle g…

We prove that for each sufficiently complicated orientable surface $S$, there exists an infinite image linear representation $\rho$ of $\pi_1(S)$ such that if $\gamma\in\pi_1(S)$ is freely homotopic to a simple closed curve on $S$, then…

We show that uniform lattices in some semi-simple groups (notably complex ones) admit Anosov surface subgroups. This result has a quantitative version: we introduce a notion, called $K$-Sullivan maps, which generalizes the notion of…

The characterization of normal subgroups M, N of free group F for which the quotient group F/[M,N] is finitely presented is given.

We are intereseted in quandles and their enveloping groups. Various results are proven. We show that a quandle $Q$ and its image in the enveloping group $G(Q)$ have isomorphic enveloping groups. The image quandle is injective. For $Q$ a…

Let $N$ be a nilpotent group normal in a group $G$. Suppose that $G$ acts transitively upon the points of a finite non-Desarguesian projective plane $\mathcal{P}$. We prove that, if $\mathcal{P}$ has square order, then $N$ must act…

We start with the observation that the quantum group SL_q(2), described in terms of its algebra of functions has a quantum subgroup, which is just a usual Cartan group. Based on this observation we develop a general method of constructing…

Let $\frak{F}$ be a class of finite groups. A subgroup $H$ of a finite group $G$ is said to be $\mathfrak{F_{\mathrm s}}$-quasinormal in $G$ if there exists a normal subgroup $T$ of $G$ such that $HT$ is $s$-permutable in $G$ and $(H\cap…

Given a smooth curve $C/\mathbb{Q}$ with genus $\geq 2$, we know by Faltings' Theorem that $C(\mathbb{Q})$ is finite. Here we ask the reverse question: given a finite set of rational points $S\subseteq \mathbb{P}^n(\mathbb{Q})$, does there…

An automorphism of an algebraic surface $S$ is called cohomologically (numerically) trivial if it acts identically on the second $l$-adic cohomology group (this group modulo torsion subgroup). Extending the results of S. Mukai and Y.…

Let $\Gamma(S)$ be the pure mapping class group of a connected orientable surface $S$ of negative Euler characteristic. For ${\mathscr C}$ a class of finite groups, let $\hat{\pi}_1(S)^{\mathscr C}$ be the pro-${\mathscr C}$ completion of…

For a oriented genus g surface with one boundary component, S, the Torelli group is the group of orientation preserving homeomorphisms of S that induce the identity on homology. The Magnus representation of the Torelli group represents the…

In this article, we study the relative negative K-groups $K_{-n}(f)$ of a map $f: X \to S $ of schemes. We prove a relative version of the Weibel conjecture i.e. if $f: X \to S$ is a smooth affine map of noetherian schemes with $\dim S=d$…

The lattice of subgroups of a group is the subject of numerous results revolving around the central theme of decomposing the group into "chunks" (subquotients) that can then be compared to one another in various ways. Examples of results in…