R. Guzman

activity

20182025

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3 papers · 1 filter

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.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…

Actualizing subgroups of 3-manifold groups in homologically small submanifolds

Hyperbolic volume, mod 2 homology, and k-freeness

The geometry of k-free hyperbolic 3-manifolds

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