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EnglishAs a consequence of a general result about finite group actions on 3‐manifolds, we show that a hyperbolic 3‐manifold can be the cyclic branched cover of at most fifteen inequivalent knots in S^3 (in fact, a main motivation of the present paper is to establish the existence of such a universal bound). A similar, though weaker, result holds for arbitrary irreducible 3‐manifolds: an irreducible 3‐manifold can be a cyclic branched cover of odd prime order of at most six knots in S^3. We note that in most other cases such a universal bound does not exist.
| Autori: | |
| Titolo: | Finite group actions on 3-manifolds and cyclic branched covers of knots |
| Digital Object Identifier (DOI): | 10.1112/topo.12052 |
| Data di pubblicazione: | 2018 |
| Abstract: | As a consequence of a general result about finite group actions on 3‐manifolds, we show that a hyperbolic 3‐manifold can be the cyclic branched cover of at most fifteen inequivalent knots in S^3 (in fact, a main motivation of the present paper is to establish the existence of such a universal bound). A similar, though weaker, result holds for arbitrary irreducible 3‐manifolds: an irreducible 3‐manifold can be a cyclic branched cover of odd prime order of at most six knots in S^3. We note that in most other cases such a universal bound does not exist. |
| Lingua: | Inglese |
| Rivista: | |
| Citazione: | Boileau, M., Franchi, C., Mecchia, M., Paoluzzi, L., Zimmermann, B., Finite group actions on 3-manifolds and cyclic branched covers of knots, <<JOURNAL OF TOPOLOGY>>, 2018; 2018 (11): 283-308. [doi:10.1112/topo.12052] [http://hdl.handle.net/10807/118954] |
| Appare nelle tipologie: | Articolo in rivista, Nota a sentenza |
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