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arXiv 2408.166352024-08math.GT

具有单个JSJ环面的SU(2)-阿贝尔图流形

SU(2)-abelian graph manifolds with a single JSJ torus

Giacomo Bascapè

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AI总结：

该研究针对粘合两个带两条奇异纤维的圆盘上Seifert纤维化空间得到的单JSJ环面图流形，依据Seifert系数完成SU(2)-阿贝尔3-流形的分类，并证明这类流形是Heegaard Floer同调L-空间。

摘要：

若一个3-流形的基本群的每个SU(2)-表示都具有阿贝尔像，则称其为SU(2)-阿贝尔的。我们针对由两个均在圆盘上纤维化且具有两条奇异纤维的Seifert空间粘合得到的图流形族，依据Seifert系数对其中的SU(2)-阿贝尔3-流形进行了分类。最后，我们证明了这些SU(2)-阿贝尔流形是Heegaard Floer同调L-空间。

英文摘要：

A 3-manifold is called \emph{SU(2)}-abelian if every SU(2)-representation of its fundamental group has abelian image. We classify, in terms of the Seifert coefficients, SU(2)-abelian 3-manifolds among the family of graph manifolds obtained by gluing two Seifert spaces both fibred over a disk and with two singular fibers. Finally, we prove that these SU(2)-abelian manifolds are Heegaard Floer homology L-spaces.

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