The Most Refined Invariant of Degree One of Knots and Links in $R^1$-Fibrations Over a Surface
| dc.creator | Tchernov, Vladimir | |
| dc.date | 1999-06-21 | |
| dc.date.accessioned | 2026-07-07T05:29:35Z | |
| dc.date.available | 2026-07-07T05:29:35Z | |
| dc.description | As it is well-known, all Vassiliev invariants of degree one of a knot $K\subset R^3$ are trivial. There are nontrivial Vassiliev invariants of degree one, when the ambient space is not $R^3$. Recently, T. Fiedler introduced such invariants of a knot in an $R^1$-fibration over a surface $F$. They take values in the free $Z$-module generated by all the free homotopy classes of loops in $F$. Here, we generalize them to the most refined Vassiliev invariant of degree one. The ranges of values of all these invariants are explicitly described. We also construct a similar invariant of a two-component link in an $\R^1$-fibration. It generalizes the linking number. | |
| dc.description | 9 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/9906137 | |
| dc.identifier | http://arxiv.org/abs/math/9906137 | |
| dc.identifier | J. Knot Theory Ramifications 7 (1998), no. 2, pp. 257-266 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78694 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25, 57M99 (Primary) | |
| dc.title | The Most Refined Invariant of Degree One of Knots and Links in $R^1$-Fibrations Over a Surface | |
| dc.type | text |