The minimal genus problem in ℂℙ2 # ℂℙ2

Ait Nouh, Mohamed

doi:10.2140/agt.2014.14.671

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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

DOI: 10.2140/agt.2014.14.671

Abstract

In this paper, we give two infinite families of counterexamples and finite positive examples to a conjecture on the minimal genus problem in $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mrow><mi>ℂ</mi><mi>ℙ</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>#</mi><msup><mrow><mi>ℂ</mi><mi>ℙ</mi></mrow><mrow><mn>2</mn></mrow></msup></math>$ 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

Volume 14, issue 2 (2014)