SU(2)-abelian 图流形的分类

arXiv - MATH - Geometric Topology Pub Date : 2024-08-29 DOI:arxiv-2408.16635

Giacomo Bascapè

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引用次数: 0

摘要

如果一个 3-manifold 的基本群的每个 SU(2)-representation 都具有非等边像，那么这个 3-manifold 就叫做 \emph{SU(2)}-abelian 。我们根据塞弗特系数，将通过粘合两个都在圆盘上有纤维且具有双倍纤维的塞弗特空间而得到的图流形家族中的 SU(2)-abelian 3-manifolds 进行分类。最后，我们证明了这些 SU(2)-abelian 流形是 Heegaard Floer homology L 空间。

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A classification of SU(2)-abelian graph manifolds

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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arXiv - MATH - Geometric Topology

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