Linking Numbers in Three-Manifolds

被引:1
|
作者
Cahn, Patricia [1 ]
Kjuchukova, Alexandra [2 ]
机构
[1] Smith Coll, Northampton, MA 01063 USA
[2] Max Planck Inst Math, Bonn, Germany
关键词
Knots; 3-manifolds; Linking numbers; INVARIANTS; KNOTS;
D O I
10.1007/s00454-021-00287-3
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
Let M be a connected, closed, oriented three-manifold and K, L two rationally null-homologous oriented simple closed curves in M. We give an explicit algorithm for computing the linking number between K and L in terms of a presentation of M as an irregular dihedral three-fold cover of S-3 branched along a knot alpha subset of S-3. Since every closed, oriented three-manifold admits such a presentation, our results apply to all (well-defined) linking numbers in all three-manifolds. Furthermore, ribbon obstructions for a knot alpha can be derived from dihedral covers of alpha. The linking numbers we compute are necessary for evaluating one such obstruction. This work is a step toward testing potential counter-examples to the Slice-Ribbon Conjecture, among other applications.
引用
收藏
页码:435 / 463
页数:29
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