R. Guzman

activity

20122025

collaborators

6 papers

math.GT2025

Actualizing subgroups of 3-manifold groups in homologically small submanifolds

Rosemary K. Guzman, Peter B. Shalen

Let $Y$ be a simple $3$ -manifold, and let $A$ be a finitely generated, freely indecomposable subgroup of $π_{1} (Y)$ . Set $η = dim H_{1} (A; F_{2})$ . Suppose that either (a) $\partial…

math.GT2022

The ratio of homology rank to hyperbolic volume, II

Rosemary K. Guzman, Peter B. Shalen

Under mild topological restrictions, we obtain new linear upper bounds for the dimension of the mod $p$ homology (for any prime $p$ ) of a finite-volume orientable hyperbolic $3$ ma…

math.GT2021

The ratio of homology rank to hyperbolic volume, I

Rosemary K. Guzman, Peter B. Shalen

We show that for every finite-volume hyperbolic $3$ -manifold $M$ and every prime $p$ we have $dim H_{1} (M; F_{p}) < 168.602 \cdot vol M$ . There are slightly strong…

math.GT2020

Hyperbolic volume, mod 2 homology, and k-freeness

Rosemary K. Guzman, Peter B. Shalen

We show that if $M$ is any closed, orientable hyperbolic $3$ -manifold with $vol M \leq 3.69$ , we have $dim H_{1} (M; F_{2}) \leq 7$ . This may be regarded as a qualitative i…

math.GT2018

The geometry of $k$ -free hyperbolic $3$ -manifolds

Rosemary K. Guzman, Peter B. Shalen

We investigate the geometry of closed, orientable, hyperbolic $3$ -manifolds whose fundamental groups are $k$ -free for a given integer $k \geq 3$ . We show that any such manifold $M$ c…

math.GT2012

Hyperbolic 3-manifolds with k-free fundamental group

Rosemary K. Guzman

The results of Culler and Shalen for 2,3 or 4-free hyperbolic 3-manifolds are contingent on properties specific to and special about rank two subgroups of a free group. Here we det…

Actualizing subgroups of 3-manifold groups in homologically small submanifolds

The ratio of homology rank to hyperbolic volume, II

The ratio of homology rank to hyperbolic volume, I

Hyperbolic volume, mod 2 homology, and k-freeness

The geometry of k-free hyperbolic 3-manifolds

Hyperbolic 3-manifolds with k-free fundamental group

The geometry of $k$ -free hyperbolic $3$ -manifolds