消失环、平面曲线奇点和框架映射类群
Vanishing cycles, plane curve singularities, and framed mapping class groups
摘要：
设f是亏格至少为5的孤立平面曲线奇点.对于所有这样的f，我们给出了（a）几何单值群的一个内在描述，它不需要引入非线性变形空间的概念，以及（b）一个简单的判据来判定Milnor纤维中给定的简单闭曲线是否为消失圈。除了$A_n$型和$D_n$型奇点外，我们发现这两种奇点都完全由与f相关的哈密顿向量场诱导的Milnor纤维的正则框架决定。作为一个推论，我们回答了一个问题的沙利文有关的单值群的注入性的所有奇异的Milnor纤维的属至少7。
英文摘要：
Let f be an isolated plane curve singularity with Milnor fiber of genus at least 5. For all such f, we give (a) an intrinsic description of the geometric monodromy group that does not invoke the notion of the versal deformation space, and (b) an easy criterion to decide if a given simple closed curve in the Milnor fiber is a vanishing cycle or not. With the lone exception of singularities of type $A_n$ and $D_n$, we find that both are determined completely by a canonical framing of the Milnor fiber induced by the Hamiltonian vector field associated to f. As a corollary we answer a question of Sullivan concerning the injectivity of monodromy groups for all singularities having Milnor fiber of genus at least 7.
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