论文标题
图形歧管及其有限盖的Seifert表示体积
Volume of Seifert representations for graph manifolds and their finite covers
论文作者
论文摘要
对于任何可定向的3个manifold，在基本组的所有SEIFERT表示空间上都定义了一个体积函数。该函数的最大绝对值与由于布鲁克斯和高盛引起的歧管的塞佛特体积一致。 对于图形歧管的任何Seifert表示，作者建立了一个有效的计算其体积的公式，并获得对代表的限制，就像Milnor-Wood不平等（关于Seifert纤维空间上的横向投射叶子）相似。结果表明，任何图形歧管的Seifert体积都是$π^2 $的合理倍数。 在给定的非几何图歧管的所有有限盖中，塞弗体积与覆盖率相比的上限比可以是正数，并且可以是无限的。发现并确认了两种可能性的示例，并确定了有限值的显式值。
For any closed orientable 3-manifold, there is a volume function defined on the space of all Seifert representations of the fundamental group. The maximum absolute value of this function agrees with the Seifert volume of the manifold due to Brooks and Goldman. For any Seifert representation of a graph manifold, the authors establish an effective formula for computing its volume, and obtain restrictions to the representation as analogous to the Milnor--Wood inequality (about transversely projective foliations on Seifert fiber spaces). It is shown that the Seifert volume of any graph manifold is a rational multiple of $π^2$. Among all finite covers of a given non-geometric graph manifold, the supremum ratio of the Seifert volume over the covering degree can be a positive number, and can be infinite. Examples of both possibilities are discovered, and confirmed, with the explicit values determined for the finite ones.
