43 citations · 184 across the 26 of their papers we have counts for
26 papers
Mapping class groups have a unique Polish group structure
Tyrone Ghaswala, Sumun Iyer, Robert Alonzo Lyman +1
We prove that mapping class groups of surfaces and of locally finite connected graphs support a unique Polish group structure.
Strongly bounded generation in transformation groups
Nicholas G. Vlamis
Word metrics on finitely generated groups have canonical quasi-isometry classes, making quasi-isometry invariants genuine group invariants. Rosendal generalized this phenomenon to…
Algebraic and geometric properties of homeomorphism groups of ordinals
Megha Bhat, Rongdao Chen, Adityo Mamun +3
We study the homeomorphism groups of ordinals equipped with their order topology, focusing on successor ordinals whose limit capacity is also a successor. This is a rich family of…
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…
Covers of surfaces
Ian Biringer, Yassin Chandran, Tommaso Cremaschi +4
We study the homeomorphism types of certain covers of (always orientable) surfaces, usually of infinite-type. We show that every surface with non-abelian fundamental group is cover…
Homeomorphism groups of telescoping 2-manifolds are strongly distorted
Nicholas G. Vlamis
Building on the work of Mann and Rafi, we introduce an expanded definition of a telescoping 2-manifold and proceed to study the homeomorphism group of a telescoping 2-manifold. Our…
Orientation-preserving homeomorphisms of Euclidean space are commutators
Megha Bhat, Nicholas G. Vlamis
We prove that every orientation-preserving homeomorphism of Euclidean space can be expressed as a commutator of two orientation-preserving homeomorphisms. We give an analogous resu…
Homeomorphism groups of 2-manifolds with the virtual Rokhlin property
Justin Lanier, Nicholas G. Vlamis
We introduce and motivate the definition of the virtual Rokhlin property for topological groups. We then classify the 2-manifolds whose homeomorphism groups have the virtual Rokhli…
Homeomorphism groups of self-similar 2-manifolds
Nicholas G. Vlamis
The class of self-similar 2-manifolds consists of manifolds exhibiting a type of homogeneity akin to the 2-sphere and the Cantor set, and includes both the 2-sphere and the 2-spher…
Bounded geometry with no bounded pants decomposition
Ara Basmajian, Hugo Parlier, Nicholas G. Vlamis
We construct a quasiconformally homogeneous hyperbolic Riemann surface-other than the hyperbolic plane-that does not admit a bounded pants decomposition. Also, given a connected or…
Mapping class groups with the Rokhlin property
Justin Lanier, Nicholas G. Vlamis
We classify the connected orientable 2-manifolds whose mapping class groups have a dense conjugacy class. We also show that the mapping class group of a connected orientable 2-mani…
Three perfect mapping class groups
Nicholas G. Vlamis
We prove that the mapping class group of a surface obtained from removing a Cantor set from either the 2-sphere, the plane, or the interior of the closed 2-disk has no proper count…
There are no exotic ladder surfaces
Ara Basmajian, Nicholas G. Vlamis
It is an open problem to provide a characterization of quasiconformally homogeneous Riemann surfaces. We show that given the current literature, this problem can be broken into fou…
Isometry groups of infinite-genus hyperbolic surfaces
Tarik Aougab, Priyam Patel, Nicholas G. Vlamis
Given a 2-manifold, a fundamental question to ask is which groups can be realized as the isometry group of a Riemannan metric of constant curvature on the manifold. In this paper,…
Ends of non-metrizable manifolds: a generalized bagpipe theorem
David Fernández-Bretón, Nicholas G. Vlamis, Mathieu Baillif
We initiate the study of ends of non-metrizable manifolds and introduce the notion of short and long ends. Using the theory developed, we provide a characterization of (non-metriza…
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.
Big mapping class groups acting on homology
Federica Fanoni, Sebastian Hensel, Nicholas G. Vlamis
We study the action of (big) mapping class groups on the first homology of the corresponding surface. We give a precise characterization of the image of the induced homology repres…
Thurston norms of tunnel number-one manifolds
Natalia Pacheco-Tallaj, Kevin Schreve, Nicholas G. Vlamis
The Thurston norm of a 3-manifold measures the complexity of surfaces representing two-dimensional homology classes. We study the possible unit balls of Thurston norms of 3-manifol…
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…
Algebraic and topological properties of big mapping class groups
Priyam Patel, Nicholas G. Vlamis
Let be an orientable, connected surface with infinitely-generated fundamental group. The main theorem states that if the genus of is finite and at least 4, then the isomorp…
Graphs of curves on infinite-type surfaces with mapping class group actions
Matthew Gentry Durham, Federica Fanoni, Nicholas G. Vlamis
We study when the mapping class group of an infinite-type surface admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on . We…
Coloring curves on surfaces
Jonah Gaster, Joshua Evan Greene, Nicholas G. Vlamis
We study the chromatic number of the curve graph of a surface. We show that the chromatic number grows like k log k for the graph of separating curves on a surface of Euler charact…
The Bridgeman-Kahn identity for hyperbolic manifolds with cusped boundary
Nicholas G. Vlamis, Andrew Yarmola
In this note, we extend the Bridgeman-Kahn identity to all finite-volume orientable hyperbolic -manifolds with totally geodesic boundary. In the compact case, Bridgeman and Kahn…
Automorphisms of the compression body graph
Ian Biringer, Nicholas G. Vlamis
When is a closed, orientable surface with genus , we show that the automorphism group of the compression body graph is the mapping class group. H…