8 papers · 1 filter
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.
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…