Non-Left-Orderable 3-Manifold Groups

[摘要] We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched coverings of $S^3$branched along links.The figure eight knot provides simple nontrivial examples. The groups arising in these examples are knownas Fibonacci groups which we show not to be left-orderable. Many other examples of non-orderable groups are obtained by taking 3-fold branched covers of $S^3$ branched along various hyperbolic 2-bridge knots. %with various hyperbolic 2-bridge knots as branched sets. The manifold obtained in such a way from the $5_2$ knotis of special interest as it is conjectured to be the hyperbolic 3-manifold with the smallest volume.

[学科分类] 数学（综合）

[关键词] Yang-Mills connection;vector bundle;gauge transformation