Thurston norm for coherent right-angled Artin groups via $L^2$-invariants
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911649537982464 |
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| author | Kudlinska, Monika |
| author_facet | Kudlinska, Monika |
| contents | We define a new notion of splitting complexity for a group $G$ along a non-trivial integral character $ϕ\in H^1(G; \mathbb{Z})$. If $G$ is a one-ended coherent right-angled Artin group, we show that the splitting complexity along an epimorphism $ϕ\colon G \to \mathbb{Z}$ equals the $L^2$-Euler characteristic of the kernel of $ϕ$. This allows us to define a Thurston-type semi-norm $\| \cdot \|_T \colon H^1(G ; \mathbb{R}) \to \mathbb{R}$ that measures the splitting complexity of integral characters. Our main tool is Friedl--Lück's $L^2$-polytope. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_02516 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thurston norm for coherent right-angled Artin groups via $L^2$-invariants Kudlinska, Monika Group Theory Geometric Topology 20F65, 20F36, 20J05, 57M60 We define a new notion of splitting complexity for a group $G$ along a non-trivial integral character $ϕ\in H^1(G; \mathbb{Z})$. If $G$ is a one-ended coherent right-angled Artin group, we show that the splitting complexity along an epimorphism $ϕ\colon G \to \mathbb{Z}$ equals the $L^2$-Euler characteristic of the kernel of $ϕ$. This allows us to define a Thurston-type semi-norm $\| \cdot \|_T \colon H^1(G ; \mathbb{R}) \to \mathbb{R}$ that measures the splitting complexity of integral characters. Our main tool is Friedl--Lück's $L^2$-polytope. |
| title | Thurston norm for coherent right-angled Artin groups via $L^2$-invariants |
| topic | Group Theory Geometric Topology 20F65, 20F36, 20J05, 57M60 |
| url | https://arxiv.org/abs/2411.02516 |