\(k\)-weakly almost convex groups and \(\pi_ 1^ \infty \widetilde M^ 3\)
If \(M^ 3\) is a closed 3-manifold such that \(\pi_ 1(M^ 3)\) is almost convex, then the first author has shown [J. Differ. Geom. 35, No. 1, 103- 130 (1992; Zbl 0777.57001)] that the universal covering space \(\widetilde{M}^ 3\) is simply-connected at infinity. In the present paper the same result is obtained under the hypothesis that \(\pi_ 1(M^ 3)\) is (only) 3-weakly almost convex, the notion referring to an upper bound of area for certain singular disks in the standard complex associated to a presentation of \(\pi_ 1(M^ 3)\).
3-weakly almost convex fundamental group
scientific article; zbMATH DE number 486899