Generalized nuclei of complex surfaces
type: Item
instance of: scholarly article
title: Generalized nuclei of complex surfaces
zbMATH Open document ID: 0927.57018
author: Terry Fuller
published in: Pacific Journal of Mathematics
publication date: 1999-12-08T00:00:00Z
review text: 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 \(g=1\)).
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 32Q99
zbMATH DE Number: 1344297
zbMATH Keywords: complex surface
zbMATH Keywords: Milnor's fibre
zbMATH Keywords: homology 3-sphere
zbMATH Keywords: handlebody description
zbMATH Keywords: nucleus
reviewed by: Athanase Papadopoulos
MaRDI profile type: Publication
full work available at URL: pjm.1999.187.281
OpenAlex ID: W2148378694
DOI: 10.2140/PJM.1999.187.281
description: scientific article; zbMATH DE number 1344297