Volume 21, issue 2 (2021)

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

Reito Nakashima

Algebraic & Geometric Topology 21 (2021) 893–916

For any positive integer g, we completely determine the minimal genus function for Σg × T2. We show that the lower bound given by the adjunction inequality is not sharp for some class in H2(Σg × T2). However, we construct a suitable embedded surface for each class and we have exact values of minimal genus functions.

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minimal genus, 4-manifolds, $T^2$–bundles, adjunction inequality
Mathematical Subject Classification 2010
Primary: 57R95
Secondary: 57R40, 57R50
Received: 7 October 2019
Revised: 8 May 2020
Accepted: 22 June 2020
Published: 25 April 2021
Reito Nakashima
Graduate School of Mathematical Sciences
The University of Tokyo