Bieri-Neumann-Strebel-Renz invariants and tropical varieties of integral homology jump loci
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912241745395712 |
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| author | Liu, Yongqiang Liu, Yuan |
| author_facet | Liu, Yongqiang Liu, Yuan |
| contents | Papadima and Suciu studied the relationship between the Bieri-Neumann-Strebel-Renz (short as BNSR) invariants of spaces and the homology jump loci of rank one local systems. Recently, Suciu improved these results using the tropical variety associated to the homology jump loci of complex rank one local systems. In particular, the translated positive-dimensional component of homology jump loci can be detected by its tropical variety. In this paper, we generalize Suciu's results to integral coefficients and give a better upper bound for the BNSR invariants. Then we provide applications mainly to Kähler groups. Specifically, we classify the Kähler group contained in a large class of groups, which we call the weighted right-angled Artin groups. This class of groups comes from the edge-weighted finite simple graphs and is a natural generalization of the right-angled Artin groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bieri-Neumann-Strebel-Renz invariants and tropical varieties of integral homology jump loci Liu, Yongqiang Liu, Yuan Geometric Topology Algebraic Geometry Papadima and Suciu studied the relationship between the Bieri-Neumann-Strebel-Renz (short as BNSR) invariants of spaces and the homology jump loci of rank one local systems. Recently, Suciu improved these results using the tropical variety associated to the homology jump loci of complex rank one local systems. In particular, the translated positive-dimensional component of homology jump loci can be detected by its tropical variety. In this paper, we generalize Suciu's results to integral coefficients and give a better upper bound for the BNSR invariants. Then we provide applications mainly to Kähler groups. Specifically, we classify the Kähler group contained in a large class of groups, which we call the weighted right-angled Artin groups. This class of groups comes from the edge-weighted finite simple graphs and is a natural generalization of the right-angled Artin groups. |
| title | Bieri-Neumann-Strebel-Renz invariants and tropical varieties of integral homology jump loci |
| topic | Geometric Topology Algebraic Geometry |
| url | https://arxiv.org/abs/2502.16026 |