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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.21729 |
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| _version_ | 1866914043864809472 |
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| author | Bascape, Giacomo |
| author_facet | Bascape, Giacomo |
| contents | We show that if $Y$ is a toroidal closed graph manifold rational homology $3$-sphere with $|H_1(Y;\mathbb{Z})| \le 5$, then there exists an irreducible representation $\fund{Y} \to SU(2)$, using topological methods and avoiding the use of gauge theory. This answers positively to a conjecture by Baldwin and Sivek in the case of graph manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21729 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Toroidal graph manifolds with small homology are not SU(2)-abelian Bascape, Giacomo Geometric Topology We show that if $Y$ is a toroidal closed graph manifold rational homology $3$-sphere with $|H_1(Y;\mathbb{Z})| \le 5$, then there exists an irreducible representation $\fund{Y} \to SU(2)$, using topological methods and avoiding the use of gauge theory. This answers positively to a conjecture by Baldwin and Sivek in the case of graph manifolds. |
| title | Toroidal graph manifolds with small homology are not SU(2)-abelian |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2506.21729 |