Related papers: Generalized Pseudo-Anosov Maps and Hubbard Trees
For an $\alpha$-expansive homeomorphism of a compact space we give an elementary proof of the following well-known result in topological dynamics: A sufficient condition for the homeomorphism to have the shadowing property is that it has…
Generalizing pseudospherical drawings, we introduce a new class of simple drawings, which we call separable drawings. In a separable drawing, every edge can be closed to a simple curve that intersects each other edge at most once. Curves of…
In this paper we study the theories of the infinite-branching tree and the $r$-regular tree, and show that both of them are pseudofinite. Moreover, we show that they can be realized by infinite ultraproducts of polynomial exact classes of…
In this work we lead with expanding maps of the circle and Anosov diffeomorphisms on $\mathbb{T}^d, d \geq 2.$ We prove that, for these maps, \textit{constant periodic data} imply \textit{same periodic data of these maps and their…
Let $M$ be a closed 3-manifold which admits an Anosov flow. In this paper we develop a technique for constructing partially hyperbolic representatives in many mapping classes of $M$. We apply this technique both in the setting of geodesic…
We define a norm on the homology of a foliated manifold, which refines and majorizes the usual Gromov norm on homology. This norm depends in an upper semi-continuous way on the underlying foliation, in the geometric topology, and can…
The Jones polynomial can be expressed in terms of spanning trees of the graph obtained by checkerboard coloring a knot diagram. We show there exists a complex generated by these spanning trees whose homology is the reduced Khovanov…
A "biased expansion" of a graph is a kind of branched covering graph with additional structure related to combinatorial homotopy of circles. Some but not all biased expansions are constructed from groups ("group expansions"); these include…
We compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set. We prove that the ratio of the number of…
In this paper, we prove several results on finitely generated dynamical Galois groups attached to quadratic polynomials. First we show that, over global fields, quadratic post-critically finite polynomials are precisely those having an…
We prove that pseudo-Anosov mapping classes are generic with respect to certain notions of genericity reflecting that we are dealing with mapping classes.
Given a finite generating set $S$, let us endow the mapping class group of a closed hyperbolic surface with the word metric for $S$. We discuss the following question: does the proportion of non-pseudo-Anosov mapping classes in the ball of…
Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound…
In [Orbit equivalences of pseudo-Anosov flows, arXiv:2211.10505], it was proved that transitive pseudo-Anosov flows on any closed 3-manifold are determined up to orbit equivalence by the set of free homotopy classes represented by periodic…
There exists a proper holomorphic mapping between balls of different dimensions such that it does not extend continuously to the boundary. The aim of this paper is to show the same phenomenon occurs for pseudoconvex domains of different…
In this paper we construct spanning trees in hyperbolic graphs that represent their hyperbolic compactification in a good way: so that the tree has a bounded number of distinct rays to each boundary point. The bound depends only on the…
We prove that generic elements of braid groups are pseudo-Anosov, in the following sense: in the Cayley graph of the braid group with n $\ge$ 3 strands, with respect to Garside's generating set, we prove that the proportion of pseudo-Anosov…
The aim of this paper is to develop a method for proving almost sure convergence in Gromov-Hausodorff-Prokhorov topology for a class of models of growing random graphs that generalises R\'emy's algorithm for binary trees. We describe the…
We introduce a new matroid (graph) invariant, the arboricity polynomial. Given a matroid, the arboricity polynomial enumerates the number of covers of the ground set by disjoint independent sets. We establish the polynomiality of the…
We show that an orientable pseudo-Anosov homeomorphism has vanishing Sah-Arnoux-Fathi invariant if and only if the minimal polynomial of its dilatation is not reciprocal. We relate this to works of Margalit-Spallone and Birman, Brinkmann…