تقرير
Classification of orientable torus bundles over closed orientable surfaces
| العنوان: | Classification of orientable torus bundles over closed orientable surfaces |
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| المؤلفون: | Kasuya, Naohiko, Noda, Issei |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, Mathematics - Algebraic Topology, Mathematics - Group Theory, 55R15, 57R22, 20F65, 57K43 |
| الوصف: | Let $g$ be a non-negative integer, $\Sigma _g$ a closed orientable surface of genus $g$, and $\mathcal{M}_g$ its mapping class group. We classify all the group homomorphisms $\pi _1(\Sigma _g)\to G$ up to the action of $\mathcal{M}_g$ on $\pi _1(\Sigma _g)$ in the following cases; (1) $G=PSL(2;\mathbb{Z})$, (2) $G=SL(2;\mathbb{Z})$. As an application of the case (2), we completely classify orientable $T^2$-bundles over closed orientable surfaces up to bundle isomorphisms. In particular, we show that any orientable $T^2$-bundle over $\Sigma _g$ with $g\geq 1$ is isomorphic to the fiber connected sum of $g$ pieces of $T^2$-bundles over $T^2$. Moreover, the classification result in the case (1) can be generalized into the case where $G$ is the free product of finite number of finite cyclic groups. We also apply it to an extension problem of maps from a closed surface to the connected sum of lens spaces. Comment: 35 pages, 12 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.14138 |
| رقم الأكسشن: | edsarx.2406.14138 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |