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On finite groups of isometries of handlebodies in arbitrary dimensions and finite extensions of Schottky groups

Mattia Mecchia, Bruno P. Zimmermann (2015)

Fundamenta Mathematicae

It is known that the order of a finite group of diffeomorphisms of a 3-dimensional handlebody of genus g > 1 is bounded by the linear polynomial 12(g-1), and that the order of a finite group of diffeomorphisms of a 4-dimensional handlebody (or equivalently, of its boundary 3-manifold), faithful on the fundamental group, is bounded by a quadratic polynomial in g (but not by a linear one). In the present paper we prove a generalization for handlebodies of arbitrary dimension d, uniformizing handlebodies...

On malnormal peripheral subgroups of the fundamental group of a 3 -manifold

Pierre de la Harpe, Claude Weber (2014)

Confluentes Mathematici

Let K be a non-trivial knot in the 3 -sphere, E K its exterior, G K = π 1 ( E K ) its group, and P K = π 1 ( ∂ E K ) ⊂ G K its peripheral subgroup. We show that P K is malnormal in G K , namely that g P K g - 1 ∩ P K = { e } for any g ∈ G K with g ∉ P K , unless K is in one of the following three classes: torus knots, cable knots, and composite knots; these are exactly the classes for which there exist annuli in E K attached to T K which are not boundary parallel (Theorem 1 and Corollary 2). More generally, we characterise malnormal peripheral subgroups in the fundamental group of a...

On manifold spines and cyclic presentations of groups

Alberto Cavicchioli, Friedrich Hegenbarth, Dušan Repovš (1998)

Banach Center Publications

This is a survey of results and open problems on compact 3-manifolds which admit spines corresponding to cyclic presentations of groups. We also discuss questions concerning spines of knot manifolds and regular neighborhoods of homotopically PL embedded compacta in 3-manifolds.

On manifolds diffeomorphic on the complement of a point

Stefano De Michelis (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove that four manifolds diffeomorphic on the complement of a point have the same Donaldson invariants.

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