4-manifolds
type: Item
instance of: scholarly article
zbMATH Open document ID: 1377.57002
author: Selman Akbulut
publication date: 2016-04-15T00:00:00Z
Mathematics Subject Classification ID: 57-02
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57Q15
Mathematics Subject Classification ID: 57R57
Mathematics Subject Classification ID: 57R65
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 55R05
zbMATH DE Number: 6569732
zbMATH Keywords: 4-manifolds
zbMATH Keywords: handlebodies
zbMATH Keywords: exotic structures
zbMATH Keywords: bundles
zbMATH Keywords: Lefschetz fibrations
zbMATH Keywords: symplectic manifolds
zbMATH Keywords: cork decomposition
zbMATH Keywords: complex surfaces
zbMATH Keywords: Seiberg-Witten invariants
MaRDI profile type: Publication
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title: 4-manifolds
published in: Oxford Graduate Texts in Mathematics
review text: Many reasons make the study of PL (or smooth) manifolds in dimension four extremely interesting, as evidenced by the numerous, significant texts that in the last decades have dealt with the subject, from different points of view: for example, [\textit{R. C. Kirby}, The topology of 4-manifolds. Berlin etc.: Springer-Verlag (1989; Zbl 0668.57001), \textit{M. H. Freedman} and \textit{F. S. Quinn}, Topology of 4-manifolds. Princeton, NJ: Princeton University Press (1990; Zbl 0705.57001) and \textit{R. E. Gompf} and \textit{A. I. Stipsicz}, 4-manifolds and Kirby calculus. Providence, RI: American Mathematical Society (1999; Zbl 0933.57020)], only to cite the most famous ones.NEWLINENEWLINEAkbulut's book provides an up-to-date overview of the subject, with a strongly original, intuitive approach. Key constructions and theorems are presented through a discursive flow of arguments, which has the vitality of true lessons, where learners are called to interact actively with the teacher. Indeed, demonstrative arguments often focus on the most meaningful passages, leaving to the reader, through suitably provided exercises, the task of completing the details not covered by the proofs. The author also performs a precise selection among the subjects, sometimes emphasizing particular cases, when their understanding is thought to be ``instructive'' in order to understand many of the difficulties appearing in the general case. In addition, most of the proofs are made through drawings, which are the real peculiarity of the text. The author himself explains this choice in the Preface: ``When there was a chance to explain some idea with pictures I always went with pictures, staying true to the saying \textit{A picture is worth a thousand words}''.NEWLINENEWLINEAlthough it is clearly stated that there is ``no attempt to cover all related results around the materials discussed'', the book succeeds in presenting a wide collection of the most significant recent results on the topology of sm…
reviewed by: Maria Rita Casali
description: scientific article; zbMATH DE number 6569732