Javier Aramayona

activity

20052026

most citedBig mapping class groups: an overview

43 citations · 217 across the 30 of their papers we have counts for

collaborators

Showing math.GTShow all

24 papers · 1 filter

math.GT2026

Asymptotically conformal and asymptotically rigid mapping class groups

Javier Aramayona, George Domat, Christopher Leininger

We give conditions ensuring that an asymptotically rigid mapping class group, specifically a surface Houghton group $H (S)$ , has finite index in the asymptotically conform…

math.GT2024

Non-planar ends are continuously unforgettable

Javier Aramayona, Rodrigo De Pool, Rachel Skipper +3

We show that continuous epimorphisms between a class of subgroups of mapping class groups of orientable infinite-genus 2-manifolds with no planar ends are always induced by homeomo…

math.GT2023

Surface Houghton groups

Javier Aramayona, Kai-Uwe Bux, Heejoung Kim +1

For every $n \geq 2$ , the {\em surface Houghton group} $B_{n}$ is defined as the asymptotically rigid mapping class group of a surface with exactly $n$ ends, all of them non-p…

math.GT2022

Block mapping class groups and their finiteness properties

Javier Aramayona, Julio Aroca, María Cumplido +2

A Cantor surface $C_{d}$ is a non-compact surface obtained by gluing copies of a fixed compact surface $Y^{d}$ (a block), with $d + 1$ boundary components, in a tree-like fashio…

math.GT2021★ 1 cited

Asymptotic mapping class groups of Cantor manifolds and their finiteness properties

Javier Aramayona, Kai-Uwe Bux, Jonas Flechsig +2

We prove that the infinite family of asymptotic mapping class groups of surfaces of defined by Funar--Kapoudjian and Aramayona--Funar are of type $F_{\infty}$ , thus answering questio…

math.GT2021

Matching arc complexes: connectedness and hyperbolicity

Javier Aramayona, Rodrigo de Pool, Alejandro Fernández

Addressing a question of Zaremsky, we give conditions on a finite simplicial graph which guarantee that the associated matching arc complex is connected and hyperbolic.

math.GT2021

Big mapping class groups and the co-Hopfian property

Javier Aramayona, Christopher J. Leininger, Alan McLeay

We study injective homomorphisms between big mapping class groups of infinite-type surfaces. First, we construct (uncountably many) examples of surfaces without boundary whose (pur…

math.GT2020★ 43 cited

Big mapping class groups: an overview

Javier Aramayona, Nicholas G. Vlamis

We survey recent developments on mapping class groups of surfaces of infinite topological type.

math.GT2018

Big Torelli groups: generation and commensuration

Javier Aramayona, Tyrone Ghaswala, Autumn E. Kent +3

For any surface $Σ$ of infinite topological type, we study the Torelli subgroup $I (Σ)$ of the mapping class group $MCG (Σ)$ , whose elements are those mapping classe…

math.GT2018★ 6 cited

Quotients of the mapping class group by power subgroups

Javier Aramayona, Louis Funar

We study the quotient of the mapping class group $Mod_{g}^{n}$ of a surface of genus $g$ with $n$ punctures, by the subgroup $Mod_{g}^{n} [p]$ generated by the…

math.GT2017★ 34 cited

The first integral cohomology of pure mapping class groups

Javier Aramayona, Priyam Patel, Nicholas G. Vlamis

It is a classical result of Powell that pure mapping class groups of connected, orientable surfaces of finite type and genus at least three are perfect. In stark contrast, we const…

math.GT2017

Asymptotic mapping class groups of closed surfaces punctured along Cantor sets

Javier Aramayona, Louis Funar

We introduce subgroups $B_{g} < H_{g}$ of the mapping class group $M o d (Σ_{g})$ of a closed surface of genus $g \geq 0$ with a Cantor set removed, which are extension…

math.GT2015

Arc and curve graphs for infinite-type surfaces

Javier Aramayona, Ariadna Fossas, Hugo Parlier

We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it…

math.GT2014★ 16 cited

Exhausting curve complexes by finite rigid sets

Javier Aramayona, Christopher J. Leininger

Let $S$ be a connected orientable surface of finite topological type. We prove that there is an exhaustion of the curve complex $C (S)$ by a sequence of finite rigid sets.

math.GT2014

Injective maps between flip graphs

Javier Aramayona, Thomas Koberda, Hugo Parlier

We prove that every injective simplicial map $F (S) \to F (S^{'})$ between flip graphs is induced by a subsurface inclusion $S \to S^{'}$ , except in finitely many cases.…

math.GT2013★ 24 cited

The proper geometric dimension of the mapping class group

Javier Aramayona, Conchita Martínez-Pérez

We show that the mapping class group of a closed surface admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension.

math.GT2012

Finite rigid sets in curve complexes

Javier Aramayona, Christopher J. Leininger

We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex X of the curve complex C(S)…

math.GT2011

Convexity of strata in diagonal pants graphs of surfaces

Javier Aramayona, Cyril Lecuire, Hugo Parlier +1

We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson compl…

math.GT2010★ 21 cited

Homomorphisms between mapping class groups

Javier Aramayona, Juan Souto

Suppose that $X$ and $Y$ are surfaces of finite topological type, where $X$ has genus $g \geq 6$ and $Y$ has genus at most $2 g - 1$ ; in addition, suppose that $Y$ is not closed if it…

math.GT2009

Simplicial embeddings between pants graphs

Javier Aramayona

We prove that, except in some low-complexity cases, every locally injective simplicial map between pants graphs is induced by a $π_{1}$ -injective embedding between the corresponding…

math.GT2008★ 41 cited

Injections of mapping class groups

Javier Aramayona, Christopher J. Leininger, Juan Souto

We construct new monomorphisms between mapping class groups of surfaces. The first family of examples injects the mapping class group of a closed surface into that of a different c…

math.GT2007

Constructing convex planes in the pants complex

Javier Aramayona, Hugo Parlier, Kenneth J. Shackleton

Our main theorem identifies a class of totally geodesic subgraphs of the 1-skeleton of the pants complex, each isomorphic to the product of two Farey graphs. We deduce the existenc…

math.GT2006

Totally geodesic subgraphs of the pants complex

Javier Aramayona, Hugo Parlier, Kenneth J. Shackleton

Our main theorem asserts that every Farey graph embedded in the 1-skeleton of the pants complex of any finite type surface is totally geodesic.

math.GT2005★ 11 cited

A simple criterion for non-relative hyperbolicity and one-endedness of groups

James W. Anderson, Javier Aramayona, Kenneth J. Shackleton

We give a combinatorial criterion that implies both the non-strong relative hyperbolicity and the one-endedness of a finitely generated group. We use this to show that many importa…