Linking numbers in rational homology 3-spheres, cyclic branched covers and infinite cyclic covers
| dc.creator | Przytycki, Jozef H. | |
| dc.creator | Yasuhara, Akira | |
| dc.date | 2001-11-19 | |
| dc.date.accessioned | 2026-07-07T04:44:40Z | |
| dc.date.available | 2026-07-07T04:44:40Z | |
| dc.description | We study the linking numbers in a rational homology 3-sphere and in the infinite cyclic cover of the complement of a knot. They take values in $\Bbb Q$ and in ${Q}({\Bbb Z}[t,t^{-1}])$ respectively, where ${Q}({\Bbb Z}[t,t^{-1}])$ denotes the quotient field of ${\Bbb Z}[t,t^{-1}]$. It is known that the modulo-$\Bbb Z$ linking number in the rational homology 3-sphere is determined by the linking matrix of the framed link and that the modulo-${\Bbb Z}[t,t^{-1}]$ linking number in the infinite cyclic cover of the complement of a knot is determined by the Seifert matrix of the knot. We eliminate ` modulo $\Bbb Z$' and ` modulo ${\Bbb Z}[t,t^{-1}]$'. When the finite cyclic cover of the 3-sphere branched over a knot is a rational homology 3-sphere, the linking number of a pair in the preimage of a link in the 3-sphere is determined by the Goeritz/Seifert matrix of the knot. | |
| dc.description | LaTeX, 24 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0111203 | |
| dc.identifier | http://arxiv.org/abs/math/0111203 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62681 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25 (Primary) 57M10, 57M 12 (Secondary) | |
| dc.title | Linking numbers in rational homology 3-spheres, cyclic branched covers and infinite cyclic covers | |
| dc.type | text |