Almost Convex Groups and the Eight Geometries

1993/06/16 by Michael Shapiro, Shapiro, Michael, Melany Stein +1
Computer Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/9306202

openalex publication_date 1993/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If M is a closed Nil geometry 3-manifold then π₁(M) is almost convex with respect to a fairly simple ``geometric'' generating set. If G is a central extension or a \Bbb Z-extension of a word hyperbolic group, then G is also almost convex with respect to some generating set. Combining these with previously known results shows that if M is a closed 3-manifold with one of Thurston's eight geometries, π₁(M) is almost convex with respect to some generating set if and only if the geometry in question is not Sol.

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