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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 2#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
References
Publication
Received: 24 September 2008
Revised: 8 August 2013
Accepted: 8 August 2013
Published: 30 January 2014
Authors
Mohamed Ait Nouh
Department of Mathematical Sciences
University of Texas at El Paso
500 West University Avenue
Bell Hall 144
El Paso, Texas 79968
USA