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Differential Algebraic Topology: From Stratifolds to Exotic Spheres (Graduate Studies in Mathematics, 110) ハードカバー – 2010/5/8

英語版 Matthias Kreck (著)

"This book presents a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. The author introduces a new class of stratified spaces, so-called stratifolds. He derives basic concepts from differential topology such as Sard's theorem, partitions of unity and transversality. Based on this, homology groups are constructed in the framework of stratifolds and the homology axioms are proved. This implies that for nice spaces these homology groups agree with ordinarysingular homology. Besides the standard computations of homology groups using the axioms, straightforward constructions of important homology classes are given. The author also defines stratifold cohomology groups following an idea of Quillen. Again, certain important cohomology classes occur very naturally in this description, for example, the characteristic classes which are constructed in the book and applied later on. One of the most fundamental results, Poincarâe duality, is almost a triviality in this approach. Some fundamental invariants, such as the Euler characteristic and the signature, are derived from (co)homology groups. These invariants play a significant role in some of the most spectacular results in differential topology. In particular, the author proves a special case of Hirzebruch's signature theorem and presents as a highlight Milnor's exotic 7-spheres."--Publisher's description.

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本の長さ

218ページ
言語

英語
出版社

Amer Mathematical Society
発売日

2010/5/8
寸法

19.05 x 1.91 x 26.67 cm
ISBN-10

0821848984
ISBN-13

978-0821848982
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商品の説明

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Differential Algebraic Topology: From Stratifolds to Exotic Spheres is a good book. It is clearly written, has many good examples and illustrations, and, as befits a graduate-level text, exercises. It is a wonderful addition to the literature." - MAA Reviews

"This book is a very nice addition to the existing books on algebraic topology. A careful effort has been made to give the intuitive background when a new concept is introduced. This and the choice of topics makes reading the book a real pleasure." - Marko Kranjc, Mathematical Reviews

著者について

Matthias Kreck, Hausdorff Research Institute for Mathematics, Bonn, Germany

登録情報

出版社 ‏ : ‎ Amer Mathematical Society (2010/5/8)
発売日 ‏ : ‎ 2010/5/8
言語 ‏ : ‎ 英語
ハードカバー ‏ : ‎ 218ページ
ISBN-10 ‏ : ‎ 0821848984
ISBN-13 ‏ : ‎ 978-0821848982
寸法 ‏ : ‎ 19.05 x 1.91 x 26.67 cm

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Matthias Kreck

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著者をフォロー

Differential Algebraic Topology: From Stratifolds to Exotic Spheres (Graduate Studies in Mathematics, 110) ハードカバー – 2010/5/8

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著者について

Matthias Kreck

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