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On boundary slopes of immersed incompressible surfaces

Mark D. Baker (1996)

Annales de l'institut Fourier

Let M be a compact, orientable, irreducible 3-manifold with M a torus. We show that there can be infinitely many slopes on M realized by the boundary curves of immersed, incompressible, - incompressible surfaces in M which are embedded in a neighborhood of M .

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.

Currently displaying 241 – 260 of 454