Michael C. Kopreski

activity

20182025

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5 papers · 1 filter

math.GT2025

Geometric models and asymptotic dimension for infinite-type surface mapping class groups

Michael C. Kopreski, George Shaji

Let $S$ be an infinite-type surface and let $G \leq Map (S)$ be a locally bounded Polish subgroup. We construct a metric graph $M$ of simple arcs and curves on $S$ pr…

math.GT2024

Automorphisms of the sphere complex of an infinite graph

Thomas Hill, Michael C. Kopreski, Rebecca Rechkin +2

For a locally finite, connected graph $Γ$ , let $Map (Γ)$ denote the group of proper homotopy equivalences of $Γ$ up to proper homotopy. Excluding sporadic cases, we s…

math.GT2024

The asymptotic dimension of the grand arc graph is infinite

Michael C. Kopreski

Let $Σ$ be a compact, orientable surface of genus $g$ , and let $Γ$ be a relation on $π_{0} (\partial Σ)$ such that the prescribed arc graph $A (Σ, Γ)$ is Gromov-hyperbolic and…

math.GT2023

Multiarc and curve graphs are hierarchically hyperbolic

Michael C. Kopreski

A multiarc and curve graph is a simplicial graph whose vertices are arc and curve systems on a compact, connected, orientable surface S. We show that all connected, non-trivial mul…

math.GT2023

Prescribed Arc Graphs

Michael C. Kopreski

Given a compact surface $Σ$ with boundary and a relation $Γ$ on $π_{0} (\partial Σ)$ , we define the prescribed arc graph $A (Σ, Γ)$ to be the full subgraph of the arc graph $\ma…