Volume 14, issue 2 (2014)

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The minimal genus problem in $\mathbb{C\mskip-1mu P}^2 \mathbin{\#} \mathbb{C\mskip-1mu P}^2$

Mohamed Ait Nouh

Algebraic & Geometric Topology 14 (2014) 671–686
Abstract

In this paper, we give two infinite families of counterexamples and finite positive examples to a conjecture on the minimal genus problem in ${ℂℙ}^{2}#{ℂℙ}^{2}$ proposed by Lawson [Exposition. Math. 15 (1997) 385–431].

Keywords
minimal genus problem, $\mathbb{CP}^2$–genus, twisting operation
Mathematical Subject Classification 2010
Primary: 57Q25
Secondary: 57Q45, 57N70