Related papers: An infinite presentation of the Torelli group

In this paper, generalising the idea of the Rokhlin property, we explore the concept of the twisted Rokhlin property of topological groups. A topological group is said to exhibit the twisted Rokhlin property if, for each automorphism $\phi$…

A topological group $G$ is topologically normally generated if there exists $g \in G$ such that the normal closure of $g$ is dense in $G$. Let $S$ be a tame, infinite type surface whose mapping class group $\mathrm{Map}(S)$ is generated by…

Consider a connected orientable surface $S$ of infinite topological type, i.e. with infinitely-generated fundamental group. We describe the large-scale geometry of arbitrary connected subgraphs of the arc complex $A(S)$ and curve complex…

We show that Szepietowski's system of generators for the mapping class group of a non-orientable surface is a minimal generating set by Dehn twists and $Y$-homemorphisms.

In this paper we introduce, for each closed orientable surface, an analogue of Tits buildings adjusted to investigation of the Torelli group of this surface. It is a simplicial complex with some additional structure. We call this complex…

We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…

The computation of the fundamental group of the complement of an algebraic plane curve has been theoretically solved since Zariski-van Kampen, but actual computations are usually cumbersome. In this work, we describe the notion of Wirtinger…

A mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies. In the published version of "Mapping class group and a global Torelli theorem for hyperkahler manifolds" I made an error based on a…

In this article we determine, for an infinite family of maps on the plane, the topology of the surface on which the minimal regular covering occurs. This infinite family includes all Archimedean maps.

This article is a revised version of the talk I gave at the conference ``Beauville Surfaces and groups'' held in Newcastle in June 2012. It presents some group theoretical methods to give bounds on the number of connected components of the…

Let $\mathcal G$ denote the space of finitely generated marked groups. For any finitely generated group $G$, we construct a continuous, injective map $f$ from the space of subgroups $Sub(G)$ to $\mathcal G$ that sends conjugate subgroups to…

We study infinite superelliptic curves as translation surfaces and explore their Veech groups. These objects are branched covering of the complex plane with branching over infinitely many points. We provide a criterion for isomorphism…

Groups of almost upper triangular infinite matrices with entries indexed by integers are studied. It is shown that, when the matrices are over a finite field, these groups admit a nondiscrete totally disconnected, locally compact group…

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…

We show that the closure of the compactly supported mapping class group of an infinite-type surface is not generated by the collection of multitwists (i.e. products of powers of twists about disjoint non-accumulating curves).

We give a new proof of a celebrated theorem of Dennis Johnson that asserts that the kernel of the Johnson homomorphism on the Torelli subgroup of the mapping class group is generated by separating twists. In fact, we prove a more general…

Let S be a connected, compact and orientable surface of genus two having exactly one boundary component. We study automorphisms of the Torelli complex for S, and describe any isomorphism between finite index subgroups of the Torelli group…

In this short note we prove a version of Bertini's theorem for unipotent rigid fundamental groups, stating that for every smooth, projective, geometrically connected variety $X$ over an infinite perfect field $k$ of characteristic $p>0$,…

We obtain simple generating sets for various mapping class groups of a nonorientable surface with punctures and/or boundary. We also compute the abelianizations of these mapping class groups.

We prove that every finitely generated group with recursive aspherical presentation embeds into a group with finite aspherical presentation. This and several known facts about groups and manifolds imply that there exists a 4-dimensional…