Minimal genus problem for $T^{2}$-bundles over surfaces

Reito Nakashima

doi:10.2140/agt.2021.21.893

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arXiv · 1902.05240

Minimal genus problem for $T^{2}$-bundles over surfaces

Reito Nakashima

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Abstract

For any positive integer $g$, we completely determine the minimal genus function for $\Sigma_{g}\times T^{2}$. We show that the lower bound given by the adjunction inequality is not sharp for some class in $H_{2}(\Sigma_{g}\times T^{2})$. However, we construct a suitable embedded surface for each class and we have exact values of minimal genus functions.

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BibTeX RIS

Reito Nakashima. 2019-02-14. Minimal genus problem for $T^{2}$-bundles over surfaces. https://doi.org/10.2140/agt.2021.21.893

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