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Lawson, H. Blaine 作者

American Mathematical Society

译者

1985-12-31 出版日期

101 页数

USD 27 价格

Pap

Conference Board of the Mathematical Sciences 丛书系列

9780821807088 图书编码

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The Theory of Gauge Fields in Four Dimensions 在线电子书 pdf 下载 txt下载 epub 下载 mobi 在线电子书下载

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Lawson's expository lectures, presented at a CBMS Regional Conference held in Santa Barbara in August 1983, provide an in-depth examination of the recent work of Simon Donaldson, and is of special interest to both geometric topologists and differential geometers. This work has excited particular interest, in light of Mike Freedman's recent profound results: the complete classification, in the simply connected case, of compact topological 4-manifolds. Arguing from deep results in gauge field theory, Donaldson has proved the nonexistence of differentiable structures on certain compact 4-manifolds. Together with Freedman's results, Donaldson's work implies the existence of exotic differentiable structures in $mathbb R^4$-a wonderful example of the results of one mathematical discipline yielding startling consequences in another. The lectures are aimed at mature mathematicians with some training in both geometry and topology, but they do not assume any expert knowledge. In addition to a close examination of Donaldson's arguments, Lawson also presents, as background material, the foundation work in gauge theory (Uhlenbeck, Taubes, Atiyah, Hitchin, Singer, et al.) which underlies Donaldson's work.

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