Generalized nuclei of complex surfaces
The author studies, for each \(g\geq 1\), a family \(Y_g(n)\) of complex surfaces admitting a singular fibration over \(CP^1\) by genus \(g\) Riemann surfaces and he describes their topology by means of the Kirby calculus. By examining a handlebody description of \(Y_g(n)\), the author shows that each of these complex surfaces \(Y_g(n)\) can be smoothly decomposed as the Milnor fibre of a Brieskorn homology 3-sphere union a small submanifold, which is called a ``nucleus''. Nuclei have been introduced by R. Gompf who discovered them as small submanifolds of elliptic surfaces which carry much of the differential topology of these larger surfaces, and Gompf has given a description of the complements of nuclei as a certain family of Milnor fibers of Brieskorn homology 3-spheres. Thus, the author's construction here is a generalization of Gompf's decomposition (which concerns the case \(g=1\)).
scientific article; zbMATH DE number 1344297