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2018•International Journal of Algebra and ComputationOpen access

Rank and Nielsen equivalence in hyperbolic extensions

Spencer Dowdall, Samuel J. Taylor

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Abstract

In this note, we generalize a theorem of Juan Souto on rank and Nielsen equivalence in the fundamental group of a hyperbolic fibered [Formula: see text]-manifold to a large class of hyperbolic group extensions. This includes all hyperbolic extensions of surfaces groups as well as hyperbolic extensions of free groups by convex cocompact subgroups of [Formula: see text].

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In this note, we generalize a theorem of Juan Souto on rank and Nielsen equivalence in the fundamental group of a hyperbolic fibered [Formula: see text]-manifold to a large class of hyperbolic group extensions. This includes all hyperbolic extensions of surfaces groups as well as hyperbolic extensions of free groups by convex cocompact subgroups of [Formula: see text].

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Available abstract

In this note, we generalize a theorem of Juan Souto on rank and Nielsen equivalence in the fundamental group of a hyperbolic fibered [Formula: see text]-manifold to a large class of hyperbolic group extensions. This includes all hyperbolic extensions of surfaces groups as well as hyperbolic extensions of free groups by convex cocompact subgroups of [Formula: see text].

Key concepts: Hyperbolic manifold, Relatively hyperbolic group, Hyperbolic group, Hyperbolic 3-manifold, Mathematics, Rank (graph theory), Equivalence (formal languages), Pure mathematics

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