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

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.

20 pages, 8 figures

References in corpus (1)

• Minimal genus in circle bundles over 3-manifolds

Cited by in corpus (1)

• The Minimal Genus Problem