Wild knots in higher dimensions as limit sets of Kleinian groups

Author:

Boege Margareta,Hinojosa Gabriela,Verjovsky Alberto

Abstract

In this paper we construct infinitely many wild knots, S n S n + 2 \mathbb {S}^{n}\hookrightarrow \mathbb {S}^{n+2} , for n = 1 , 2 , 3 , 4 n=1,2,3,4 and 5 5 , each of which is a limit set of a geometrically finite Kleinian group. We also describe some of their properties.

Publisher

American Mathematical Society (AMS)

Subject

Geometry and Topology

Reference37 articles.

1. Ordway Professorship Lectures in Mathematics;Ahlfors, Lars V.,1981

2. E. Artin. Zur Isotopie zweidimensionalen Flächen im 𝑅₄, Abh. Math. Sem. Univ. Hamburg (1926), 174-177.

3. Quickly unknotting topological spheres;Brakes, W. R.;Proc. Amer. Math. Soc.,1978

4. Nontrivial cobordisms with geometrically finite hyperbolic structures;Apanasov, B. N.;J. Differential Geom.,1988

5. Some curious Kleinian groups and hyperbolic 5-manifolds;Belegradek, I.;Transform. Groups,1997

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