The Wild World of 4-Manifolds (amsns AMS non-series title)

The Wild World of 4-Manifolds (amsns AMS non-series title)

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Titre:The Wild World of 4-Manifolds (amsns AMS non-series title)
La langue:Français
Nom de fichier:The Wild World of 4-Manifolds (amsns AMS non-series title) PDF EPUB AUDIOBOOK
ISBN:0821837494
Date de sortie:May 30, 2005
Nombre de pages:609 pages
Auteur:Alexandru Scorpan
Éditeur:American Mathematical Society

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This book offers a panorama of the topology of simply-connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but too small to have room to undo them. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. The first part of the book puts things in context with a survey of higher dimensions and of topological 4-manifolds. The second part investigates the main invariant of a 4-manifold--the intersection form--and its interaction with the topology of the manifold. The third part reviews complex surfaces as an important source of examples. The fourth and final part of the book presents gauge theory. This differential-geometric method has brought to light the unwieldy nature of smooth 4-manifolds; and although the method brings new insights, it has raised more questions than answers.The structure of the book is modular and organized into a main track of approximately 200 pages, which are augmented with copious notes at the end of each chapter, presenting many extra details, proofs, and developments.To help the reader, the text is peppered with 250 illustrations and has an extensive index.

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4 manifold Topological 4 manifolds. The homotopy type of a simply connected compact 4 manifold only depends on the intersection form on the middle dimensional homology.
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