Dehn twists and free subgroups of symplectic mapping class groups
Dehn twists and free subgroups of symplectic mapping class groups
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Dehn 扭曲和辛映射类群的自由子群
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发表时间：
2012
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通讯作者：
Ailsa Keating
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作者：
Ailsa Keating
给定一个正合辛流形中的两个拉格朗日球面，我们找到了关于它们的Dehn扭曲生成辛映射类群的一个自由非阿贝尔子群的条件。这推广了Ishida关于Riemann曲面的一个结果“由两个Dehn扭生成的映射类群的子群的结构”，Proc. Japan Acad.数学科学A系72（1996）240-241]。该证明将Seidel的长正合序列的范畴化版本[A long exact sequence for symplectic Floer cohomology '，Topology 42（2003）1003-1063]推广到固定Dehn扭的任意幂。我们还表明，任何孤立的退化超曲面奇点的Milnor纤维包含这样的球对。
Given two Lagrangian spheres in an exact symplectic manifold, we find conditions under which the Dehn twists about them generate a free non‐abelian subgroup of the symplectic mapping class group. This extends a result of Ishida for Riemann surfaces [‘The structure of subgroup of mapping class groups generated by two Dehn twists’, Proc. Japan Acad. Ser. A Math. Sci. 72 (1996) 240–241]. The proof generalizes the categorical version of Seidelˈs long exact sequence [‘A long exact sequence for symplectic Floer cohomology’, Topology 42 (2003) 1003–1063] to arbitrary powers of a fixed Dehn twist. We also show that the Milnor fibre of any isolated degenerate hypersurface singularity contains such pairs of spheres.