On Generalized Knot Groups
| dc.creator | Lin, Xiao-Song | |
| dc.creator | Nelson, Sam | |
| dc.date | 2004-07-04 | |
| dc.date | 2006-10-26 | |
| dc.date.accessioned | 2026-07-07T09:56:03Z | |
| dc.date.available | 2026-07-07T09:56:03Z | |
| dc.description | Generalized knot groups G_n(K) were introduced first by Wada and Kelly independently. The classical knot group is the first one G_1(K) in this series of finitely presented groups. For each natural number n, G_1(K) is a subgroup of G_n(K) so the generalized knot groups can be thought of as extensions of the classical knot group. For the square knot SK and the granny knot GK, we have an isomorphism $G_1(SK)\cong G_1(GK)$. From the presentations of G_n(SK) and G_n(GK), for n>1, it seems unlikely that G_n(SK) and G_n(GK) would be isomorphic to each other. We are able to show that for many finite groups H, the numbers of homomorphisms from G_n(SK) and G_n(GK) to H, respectively, are the same. Moreover, the numbers of conjugacy classes of homomorphisms from G_n(SK) and G_n(GK) to H, respectively, are also the same. It remains a challenge to us to show, as we would like to conjecture, that G_n(SK) and G_n(GK) are not isomorphic to each other for all n>1. | |
| dc.description | 7 pages, to appear in J. Knot Theory Ramifications. Version 3 includes corrections to the section on counting homomorphisms to finite groups | |
| dc.identifier | https://arxiv.org/abs/math/0407050 | |
| dc.identifier | http://arxiv.org/abs/math/0407050 | |
| dc.identifier | J. Knot Theory Ramifications 17 (2008) 263-272. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166844 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 57M27; 20F65 | |
| dc.title | On Generalized Knot Groups | |
| dc.type | text |