Fintushel, Ronald; Stern, Ronald J. Immersed spheres in 4-manifolds and the immersed Thom conjecture. (English) Zbl 0869.57016 Turk. J. Math. 19, No. 2, 145-157 (1995). The classical Thom conjecture states that the genus of a smoothly embedded surface \(F\) in \(CP^2\) representing \(d\) times the generator \(H\) of \(H_2 (CP^2;Z)\) must satisfy \(g(F) \geq(d-1) (d-2)/2\). Representing 2-dimensional homology classes by immersed 2-spheres one arrives at the Immersed Thom Conjecture: Suppose that a 2-sphere \(S\) is immersed in \(CP^2\) with \(p\) positive double points, and suppose that its image represents \(dH \in H_2 (CP^2,Z)\). Then \(p\geq (d-1) (d-2)/2\). The authors give a proof of this conjecture. Reviewer: M.Anastasiei (Iaşi) Cited in 2 ReviewsCited in 53 Documents MSC: 57N12 Topology of the Euclidean \(3\)-space and the \(3\)-sphere (MSC2010) Keywords:Seiberg-Witten theory; immersed spheres; 4-manifolds; Thom conjecture PDFBibTeX XMLCite \textit{R. Fintushel} and \textit{R. J. Stern}, Turk. J. Math. 19, No. 2, 145--157 (1995; Zbl 0869.57016)