Smooth minimal genera for small negative classes in \({\mathbb C}P^{2}{\#}n{\overline{{\mathbb C}P}^2}\) with \(n {\leqslant} 9\)

DOI10.1016/S0166-8641(02)00357-7zbMath1028.57033MaRDI QIDQ1398691

Bang-He Li, Tian-Jun Li

Publication date: 7 August 2003

Published in: Topology and its Applications (Search for Journal in Brave)

zbMATH Keywords

minimal genusStiefel-Whitney classclosed surfacefour dimensional manifoldsnegative squareadjunction inequalitiesgenus inequalities

Mathematics Subject Classification ID

Related Items (7)

The minimal genus problem in rational surfaces \(CP^2 \sharp n\overline{CP^2}\) ⋮ Stability and existence of surfaces in symplectic 4-manifolds with \(b^+=1\) ⋮ The minimal genus problem for elliptic surfaces ⋮ Kodaira dimension of fiber sums along spheres ⋮ The minimal genus problem -- a quarter century of progress ⋮ Minimal genus and simplified classes in rational manifolds ⋮ The \(E_{8}\)-boundings of homology spheres and negative sphere classes in \(E(1)\)

Cites Work

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• Positive 2-spheres in 4-manifolds of signature \((1,n)\)
• Symplectic genus, minimal genus and diffeomorphisms
• Two-dimensional submanifolds of four-dimensional manifolds
• Representing homology classes of \(CP^ 2{\#}\overline{CP}\) 2
• Smooth embeddings of 2-spheres in 4-manifolds
• A product formula for the Seiberg-Witten invariants and the generalized Thom conjecture
• Minimal genus embeddings in \(S^ 2\)-bundles over surfaces
• The minimal genus problem
• Minimal genus smooth embeddings in \(S^2\times S^2\) and \(CP^2\# n\overline{CP^2}\) with \(n\leq 8\)
• The genus of embedded surfaces in the projective plane
• Symplectic structure on ruled surfaces and a generalized adjunction formula
• The symplectic Thom conjecture
• ON 2-SPHERES IN 4-MANIFOLDS
• Representing nonnegative homology classes of ℂℙ²#𝕟\overline{ℂℙ}² by minimal genus smooth embeddings
• Representing Positive Homology Classes of $CP^2{\tt \#}2\overline{CP}^2$ and $CP^2{\tt \#}3\overline{CP}^2$
• Diffeomorphisms of 4-Manifolds
• Representing homology classes of almost definite 4-manifolds
• Representing homology classes of almost definite 4-manifolds

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