Related papers: Omnipersistent signatures

The topological data of a group action on a compact Riemann surface is often encoded using a tuple $(h;m_1,\dots ,m_s)$ called its signature. There are two easily verifiable arithmetic conditions on a tuple necessary for it to be a…

This paper focuses on the classification of classes of topological equivalence of finite group actions on Riemann surfaces. By the Riemann-Hurwitz bound, there are just finitely many groups that act conformally on a closed orientable…

We classify up to signature all the ways the alternating group $A_n$ can act on a compact Riemann surfaces when the quotient genus is greater than $0$. In particular, we prove that for $A_n$ with $n>6$ every potential signature for the…

We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus $\sigma \geq 2$ is at least quadratic in $\sigma$. We do this through the introduction of a coarse signature space, the space…

Consider a finite group $G$ acting on a Riemann surface $S$, and the associated branched Galois cover $\pi_G:S \to Y=S/G$. We introduce the concept of geometric signature for the action of $G$, and we show that it captures the information…

We describe an algorithm that constructs a list of all topological types of holomorphic actions of a finite group on a compact Riemann surface $C$ of genus at least $g \geq 2$ with $C/G \cong \mathbb{P}^1$.

Skeletal signatures were introduced in [J W Anderson and A Wootton, A Lower Bound for the Number of Group Actions on a Compact Riemann Surface, Algebr. Geom. Topol. 12 (2012) 19--35.] as a tool to describe the space of all signatures with…

This short note presents a peculiar generalization of the Riemann hypothesis, as the action of the permutation group on the elements of continued fractions. The problem is difficult to attack through traditional analytic techniques, and…

An action of a finite group $G$ is a pair $(S,\hat{G})$, where $S$ is a compact Riemann surface of genus $g \geqslant 2$ and $\hat{G} \leqslant {\rm Aut}(S)$ is isomorphic to $G$. To each action $(S,\hat{G})$ there is associated a signature…

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…

This article deals with dihedral group actions on compact Riemann surfaces and the interplay between different geometric data associated to them. First, a bijective correspondence between geometric signatures and analytic representations is…

We determine all finite maximal elementary abelian group actions on compact oriented surfaces of genus $\sigma\geq 2$ which are unique up to topological equivalence. For certain special classes of such actions, we determine group extensions…

Let PC be the group of bijections from [0, 1[ to itself which are continuous outside a finite set. Let PC be its quotient by the subgroup of finitely supported permutations. We show that the Kapoudjian class of PC vanishes. That is, the…

In this paper we deal with branched coverings over the complement to finitely many exceptional points on the Riemann sphere having the property that the local monodromy around each of the branching points is of finite order. To such a…

The aim of this paper is to present a few versions of the Riemann-Hurwitz formula for a regular branched covering of graphs. By a graph, we mean a finite connected multigraph. The genus of a graph is defined as the rank of the first…

We construct a geometric model for the mapping class group M of a non-exceptional oriented surface of finite type and use it to show that the action of M on the compact Hausdorff space of complete geodesic laminations is topologically…

Motivated by the theory of Riemann surfaces, we classify all possibilities for finite simple groups acting faithfully on a compact Riemann surface of genus at least 2 in such a way that all non-trivial elements have at most three fixed…

The mapping class group $\mathrm{Mod}_{g, 1}$ of a surface with one marked point can be identified with an index two subgroup of $\mathrm{Aut}(\pi_1 \Sigma_g)$. For a surface of genus $g \geq 2$, we show that any action of $\mathrm{Mod}_{g,…

Given a surface of higher genus, we will look at the Weil-Petersson completion of the Teichmuller space of the surface, and will study the isometric action of the mapping class group on it. The main observation is that the geometric…

In this paper, we adapt the differential signature construction to the equivalence problem for complex plane algebraic curves under the actions of the projective group and its subgroups. Given an action of a group $G$, a signature map…