论文标题
打结的Tori不变的左旋河流
A Levine-Tristram invariant for knotted tori
论文作者
论文摘要
Echeverria最近使用尺度理论进行单数连接，在同源性$ s^1 \ times s^3 $中引入了一种平滑嵌入式圆环。我们定义了这种嵌入式圆环的新拓扑不变，类似于结节的古典左旋 - 特里斯特拉姆不变。在三维的情况下，结上的单数连接数次数又重现了莱文 - 特里斯特拉姆不变。我们计算了许多嵌入的示例的不变性，并表明我们的拓扑不变与人们对Echeverria不变的期望相同。 Langte MA随后一般都表明了这一点。
Echeverria recently introduced an invariant for a smoothly embedded torus in a homology $S^1\times S^3$, using gauge theory for singular connections. We define a new topological invariant of such an embedded torus, analogous to the classical Levine-Tristram invariant of a knot. In the 3-dimensional situation, a count of singular connections on a knot complement reproduces the Levine-Tristram invariant. We compute the invariant for a number of examples embedded tori, and show that our topological invariant is the same as what one might expect from Echeverria's invariant. Langte Ma has subsequently shown this in general.
