Theta-invariants of $\mathbb{Z}π$-homology equivalences to spherical 3-manifolds
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| Format: | Preprint |
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2025
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| _version_ | 1866914074676166656 |
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| author | Kodani, Hisatoshi Watanabe, Tadayuki |
| author_facet | Kodani, Hisatoshi Watanabe, Tadayuki |
| contents | We study Bott and Cattaneo's $Θ$-invariant of 3-manifolds applied to $\mathbb{Z}π$-homology equivalences from 3-manifolds to a fixed spherical 3-manifold. The $Θ$-invariants are defined by integrals over configuration spaces of two points with local systems and by choosing some invariant tensors. We compute upper bounds of the dimensions of the space spanned by the Bott--Cattaneo $Θ$-invariants and of that spanned by Garoufalidis and Levine's finite type invariants of type 2. The computation is based on representation theory of finite groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Theta-invariants of $\mathbb{Z}π$-homology equivalences to spherical 3-manifolds Kodani, Hisatoshi Watanabe, Tadayuki Geometric Topology Algebraic Topology 57R56, 57K31, 81Q30 We study Bott and Cattaneo's $Θ$-invariant of 3-manifolds applied to $\mathbb{Z}π$-homology equivalences from 3-manifolds to a fixed spherical 3-manifold. The $Θ$-invariants are defined by integrals over configuration spaces of two points with local systems and by choosing some invariant tensors. We compute upper bounds of the dimensions of the space spanned by the Bott--Cattaneo $Θ$-invariants and of that spanned by Garoufalidis and Levine's finite type invariants of type 2. The computation is based on representation theory of finite groups. |
| title | Theta-invariants of $\mathbb{Z}π$-homology equivalences to spherical 3-manifolds |
| topic | Geometric Topology Algebraic Topology 57R56, 57K31, 81Q30 |
| url | https://arxiv.org/abs/2507.12121 |