Paige Hillen

activity

20242026

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 $I^»$ , we construct an end-periodic homeomorphism $f : I^£ \to I^£$ with Handel-Miller stretch factor equal to $I^»$ where $I^£$ is a connected infinit…

math.GR2025

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 $I^$ of rank r. Moreover, $f$ can…

math.GR2025

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.GR2025

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 $I ¨ \in Out (F_{3})$ and show that it is realized by a "principal" fully irreducible element. We also show…

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

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

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

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( $F_{3}$ )