The wild world of 4-manifolds 新书_图书内容介绍_剧情呢
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The wild world of 4-manifolds读书介绍

类别 页数 译者 网友评分 年代 出版社
书籍 614页 2020 American Mathematical Society
定价 出版日期 最近访问 访问指数
USD 85.00 2020-02-20 … 2021-02-17 … 58
主题/类型/题材/标签
数学,4-manifold,流形,微分拓扑7,topology,Mathematics,
作者
Alexandru Scorpan      ISBN:9780821837498    原作名/别名:《》
内容和作者简介
The wild world of 4-manifolds摘要

This is 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 ...

作者简介

This is 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 over 250 illustrations and has an extensive index.

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