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This article is available for purchase or by subscription. See below.
Abstract
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For any positive integer
,
we completely determine the minimal genus function for
. We
show that the lower bound given by the adjunction inequality is not sharp for some class
in
.
However, we construct a suitable embedded surface for each class and we have exact
values of minimal genus functions.
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Keywords
minimal genus, 4-manifolds, $T^2$–bundles, adjunction
inequality
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Mathematical Subject Classification 2010
Primary: 57R95
Secondary: 57R40, 57R50
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Publication
Received: 7 October 2019
Revised: 8 May 2020
Accepted: 22 June 2020
Published: 25 April 2021
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