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| Format: | Preprint |
| Published: |
2022
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| Online Access: | https://arxiv.org/abs/2209.10145 |
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| _version_ | 1866910828899336192 |
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| author | Duan, Jianru |
| author_facet | Duan, Jianru |
| contents | For any compact orientable irreducible 3-manifold $N$ with empty or incompressible toral boundary, the twisted $L^2$-torsion is a non-negative function defined on the representation variety $\operatorname{Hom}(π_1(N),\operatorname{SL}(n,\mathbb C))$. The paper shows that if $N$ has infinite fundamental group, then the $L^2$-torsion function is strictly positive. Moreover, this torsion function is continuous when restricted to the subvariety of upper triangular representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_10145 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the positivity of twisted $L^2$-torsion for 3-manifolds Duan, Jianru Geometric Topology 57K31 For any compact orientable irreducible 3-manifold $N$ with empty or incompressible toral boundary, the twisted $L^2$-torsion is a non-negative function defined on the representation variety $\operatorname{Hom}(π_1(N),\operatorname{SL}(n,\mathbb C))$. The paper shows that if $N$ has infinite fundamental group, then the $L^2$-torsion function is strictly positive. Moreover, this torsion function is continuous when restricted to the subvariety of upper triangular representations. |
| title | On the positivity of twisted $L^2$-torsion for 3-manifolds |
| topic | Geometric Topology 57K31 |
| url | https://arxiv.org/abs/2209.10145 |