Minimal genus problem for T2–bundles over surfaces

Nakashima, Reito

doi:10.2140/agt.2021.21.893

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

Reito Nakashima

Algebraic & Geometric Topology 21 (2021) 893–916

DOI: 10.2140/agt.2021.21.893

Abstract

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

Keywords

minimal genus, 4-manifolds, $T^2$–bundles, adjunction inequality

Mathematical Subject Classification 2010

Primary: 57R95

Secondary: 57R40, 57R50

References

Publication

Received: 7 October 2019

Revised: 8 May 2020

Accepted: 22 June 2020

Published: 25 April 2021

Authors

Reito Nakashima
Graduate School of Mathematical Sciences The University of Tokyo Meguro Japan

Volume 21, issue 2 (2021)