Paige Hillen

collaborators

5 papers

math.GT2026

Every Weak Perron Number is an End-Periodic Stretch Factor

Paige Hillen, Marissa Loving, Chenxi Wu

Given any weak Perron number $λ$ , we construct an end-periodic homeomorphism $f : Σ \to Σ$ with Handel-Miller stretch factor equal to $λ$ where $Σ$ is a connected infinite-typ…

math.GR2024

A hyperbolic free-by-cyclic group determined by its finite quotients

Naomi Andrew, Paige Hillen, Robert Alonzo Lyman +1

We show that the group $⟨ a, b, c, t : a^{t} = b, b^{t} = c, c^{t} = c a^{- 1} ⟩$ is profinitely rigid amongst free-by-cyclic groups, providing the first example of a hyperbolic free-by-c…

math.GR2024

Latent symmetry of graphs and stretch factors in Out(Fr)

Paige Hillen

Every irreducible outer automorphism of the free group of rank r is topologically represented by an irreducible train track map $f$ on some graph $Γ$ of rank r. Moreover, $f$ can a…

math.GR2024

Low complexity among principal fully irreducible elements of Out( $F_{3}$ )

Naomi Andrew, Paige Hillen, Robert Alonzo Lyman +1

We find the shortest realized stretch factor for a fully irreducible $φ \in Out (F_{3})$ and show that it is realized by a "principal" fully irreducible element. We also show t…

math.GT2024

Non-Uniform Lattices of Large Systole Containing a Fixed 3-Manifold Group

Paige Hillen

Let $d$ be a square free positive integer and $Q (d)$ a totally real quadratic field over $Q$ . We show there exists an arithmetic lattice L in $SL(8,\mathbb…

Every Weak Perron Number is an End-Periodic Stretch Factor

A hyperbolic free-by-cyclic group determined by its finite quotients

Latent symmetry of graphs and stretch factors in Out(Fr)

Low complexity among principal fully irreducible elements of Out(F3​)

Non-Uniform Lattices of Large Systole Containing a Fixed 3-Manifold Group

Low complexity among principal fully irreducible elements of Out( $F_{3}$ )