Circle-valued Morse theory, Reidemeister torsion, and Seiberg-Witten invariants of 3-manifolds
Circle-valued Morse theory, Reidemeister torsion, and Seiberg-Witten invariants of 3-manifolds
复制标题
圆值莫尔斯理论、Reidemeister 挠率和 3 流形的 Seiberg-Witten 不变量
作者：
M. Hutchings;Yi
设X是闭定向黎曼流形，x（X）=0，b1（X）>0，φ：X→ S1是圆值莫尔斯函数.在对φ的一些温和的假设下，我们证明了一个公式：当dim（X）=3时，我们提出了一个与Taubes的“SW=Gromov”定理有关的猜想，并利用它推导出（对于闭流形，模符号）X的Seiberg-Witten不变量与Milnor挠率之间的Meng-Taubes关系。
Let X be a closed oriented Riemannian manifold with χ(X)=0 and b1(X)>0, and let φ : X→S1be a circle-valued Morse function. Under some mild assumptions on φ, we prove a formula relating When dim(X)=3, we state a conjecture related to Taubes’s “SW=Gromov” theorem, and we use it to deduce (for closed manifolds, modulo signs) the Meng–Taubes relation between the Seiberg-Witten invariants and the “Milnor torsion” of X.