Related papers: Genericity of pseudo-Anosov mapping classes, when …

We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. That is, if the right-angled Artin group G in Mod(S) satisfies certain conditions that imply G is…

In this paper, we study the Galois conjugates of stretch factors of pseudo-Anosov elements of the mapping class group of a surface. We show that - except in low-complexity cases - these conjugates are dense in the complex plane. For this,…

Let $S$ be a closed Riemann surface of genus $p>1$ with one point removed. In this paper, we identify those point-pushing pseudo-Anosov maps on $S$ that preserve at least one bi-infinite geodesic in the curve complex.

A generic computation of a subset $A$ of $\mathbb{N}$ is a computation which correctly computes most of the bits of $A$, but which potentially does not halt on all inputs. The motivation for this concept is derived from complexity theory,…

A generalized numerical semigroup is a submonoid of $\mathbb{N}^d$ with finite complement in it. In this work we study some properties of three different classes of generalized numerical semigroups. In particular, we prove that the first…

In this paper, we are interested in study subgroups of topologized fundamental groups and their influences on generalized covering maps. More precisely, we find some relationships between generalized covering subgroups and the other famous…

We give a model-theoretic characterization of the class of geometric theories classified by an atomic topos having enough points; in particular, we show that every complete geometric theory classified by an atomic topos is countably…

We give a complete characterization of the holonomies of strictly convex cusps and of round cusps in convex projective geometry. We build families of generalized cusps of non-maximal rank associated to each strictly convex or round cusp. We…

We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.

It is shown, that the mapping class group of a surface of the genus g > 1 admits a faithful representation into the matrix group GL (6g-6, Z). The proof is based on a categorical correspondence between the Riemann surfaces and the so-called…

In this chapter, we outline some of the many combinatorial tools developed over the past three decades for studying a pseudo-Anosov diffeomorphism of a surface by analyzing the geometry of its mapping torus. We begin with an overview of the…

We show that finitely generated, purely pseudo-Anosov subgroups of the fundamental groups of surface bundles over tori are convex cocompact as subgroups of the mapping class group via the Birman exact sequence. This generalizes the fact…

Let X be a hyperbolic surface and H the fundamental group of a hyperbolic 3-manifold that fibers over the circle with fiber X. Using the Birman exact sequence, H embeds in the mapping class group Mod(Y) of the surface Y obtained by removing…

We describe a natural isomorphism between the set of equivalence classes of pseudocycles and the integral homology groups of a smooth manifold. Our arguments generalize to settings well-suited for applications in enumerative algebraic…

V. I. Arnold [Russian Math. Surveys 26, no. 2, 1971, 29-43] constructed smooth generic families of matrices with respect to similarity transformations depending smoothly on the entries of matrices and got bifurcation diagrams of such…

We study the graphs generated when the formula for linking Markov triples is applied to general triples of integers. We find there are a finite number of equivalence classes of graphs, each with particular properties.

In this paper we prove a combination theorem for Veech subgroups of the mapping class group analogous to the first Klein-Maskit combination theorem for Kleinian groups in which two Fuchsian subgroups are amalgamated along a parabolic…

We discuss how triposes may be understood as generalizations of localic geometric morphisms.

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…

We prove several rigidity properties for random quotients of mapping class groups of surfaces, namely whose kernel is normally generated by the n-th steps of finitely many independent random walks. Firstly, we generalise a celebrated…