Related papers: Conformal Automorphism Groups, Adapted Generating …

We construct a minimal generating set of the level 2 mapping class group of a nonorientable surface of genus $g$, and determine its abelianization for $g\ge4$.

A smooth complex projective curve is called pseudoreal if it is isomorphic to its conjugate but is not definable over the reals. Such curves, together with real Riemann surfaces, form the real locus of the moduli space $\mathcal M_g$. This…

By an automorphism of a topological group G we mean an isomorphism of G onto itself which is also a homeomorphism. In this article, we study the automorphism group Aut(G) of a dense subgroup G of R^n, n>=1. We show that Aut(G) can be…

In this paper we determine all finite groups G that can act on some compact Riemann surface M with the property that if H is any non-trivial subgroup of G, then the orbit surface M/H is the Riemann sphere. The idea is to look at the induced…

Let $X$ be a compact Riemann surface of genus $g\geq 2$. A cyclic subgroup of prime order $p$ of $Aut(X)$ is called properly $(p,h)$-gonal if it has a fixed point and the quotient surface has genus $h$. We show that if $p>6h+6$, then a…

If $p$ is prime, a compact Riemann surface $X$ of genus $g\geq 2$ is called cyclic $p$-gonal if it admits a cyclic group of automorphisms $C_{p}$ of order $p$ such that the quotient space $X/C_{p}$ has genus 0. If in addition $C_{p}$ is not…

The genus spectrum of a finite group $G$ is the set of all $g\geq 2$ such that $G$ acts faithfully and orientation-preserving on a closed compact orientable surface of genus $g$. This article is an overview of some results relating the…

We consider a finitely generated group acting minimally on a compact space by homeomorphsims, and assume that the Schreier graph of at least one orbit is quasi-isometric to a line. We show that the topological full group of such an action…

A Riemann surface $\mathcal{S}$ having field of moduli $\mathbb{R}$, but not a field of definition, is called \emph{pseudoreal}. This means that $\mathcal{S}$ has anticonformal automorphisms, but non of them is an involution. We call a…

A topological group $G$ is extremely amenable if every continuous action of $G$ on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of…

We define a family of groups that include the mapping class group of a genus g surface with one boundary component and the integral symplectic group Sp(2g,Z). We then prove that these groups are finitely generated. These groups, which we…

Herein we prove that if $M$ is a compact oriented Riemann surface of genus $g$, and $M^{[n]}$ is the classifying space of $n$ distinct, unordered points on $M$, then the kernel of the map $\pi_1(M^{[n]})\to H_1(M)$ is generated by…

A group action is said to be highly-transitive if it is $k$-transitive for every $k \ge 1$. The main result of this thesis is the following: Main Theorem: The fundamental group of a closed, orientable surface of genus > 1 admits a…

The special linear groups, the mapping class groups of surfaces, the outer autormorphism groups of free groups appear in numerous domains. Their analogies, developped in particular in K. Vogtmann's work, have been written about a lot. In…

A crosscap transposition is an element of the mapping class group of a nonorientable surface represented by a homeomorphism supported on a one-holed Klein bottle and swapping two crosscaps. We prove that the mapping class group of a compact…

Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…

The mapping class group of a surface with one boundary component admits numerous interesting representations including as a group of automorphisms of a free group and as a group of symplectic transformations. Insofar as the mapping class…

By a map we mean a $2$-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which…

Gaussian graphical models have become a well-recognized tool for the analysis of conditional independencies within a set of continuous random variables. From an inferential point of view, it is important to realize that they are composite…

We determine, for all genus $g\geq2$ the Riemann surfaces of genus $g$ with $4g$ automorphisms. For $g\neq$ $3,6,12,15$ or $30$, this surfaces form a real Riemann surface $\mathcal{F}_{g}$ in the moduli space $\mathcal{M}_{g}$: the Riemann…