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Titlebook: Cohomology Theories for Compact Abelian Groups; Karl H. Hofmann,Paul S. Mostert Textbook 19731st edition VEB Deutscher Verlag der Wissensc

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發(fā)表于 2025-3-21 17:44:55 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Cohomology Theories for Compact Abelian Groups
編輯Karl H. Hofmann,Paul S. Mostert
視頻videohttp://file.papertrans.cn/230/229257/229257.mp4
圖書封面Titlebook: Cohomology Theories for Compact Abelian Groups;  Karl H. Hofmann,Paul S. Mostert Textbook 19731st edition VEB Deutscher Verlag der Wissensc
描述Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo- metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again playa role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory. A particularly well understood subclass of compact groups is the class of com- pact abelian groups. An added element of elegance is the duality theory, which states that the category of compact abelian groups is completely equivalent to the category of (discrete) abelian groups with all arrows reversed. This allows for a virtually complete algebraisation of any question concerning compact abelian groups. The subclass of compact abelian groups is not so special within the category of compact. groups as it may seem at first glance. As is very well know
出版日期Textbook 19731st edition
關(guān)鍵詞Abelian group; Algebraic structure; Cohomology; Group theory; Representation theory
版次1
doihttps://doi.org/10.1007/978-3-642-80670-4
isbn_softcover978-3-642-80672-8
isbn_ebook978-3-642-80670-4
copyrightVEB Deutscher Verlag der Wissenschaften, Berlin 1973
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沙發(fā)
發(fā)表于 2025-3-21 22:11:34 | 只看該作者
The cohomology of classifying spaces of compact groups,d .—, ., where . is the algebraic cohomology with trivial action discussed in Chapter II. The reader may read Chapter VI (the appendix by E. Nummela) in conjunction with the current material; there he will find an alternate functorial construction of a classifying space.
板凳
發(fā)表于 2025-3-22 01:03:12 | 只看該作者
地板
發(fā)表于 2025-3-22 05:37:52 | 只看該作者
5#
發(fā)表于 2025-3-22 11:14:42 | 只看該作者
Sentiment Analysis in the Medical Domainat the ?ech cohomology of a compact group space is the Kan extension of any of the standard cohomologies on manifolds applied to Lie group spaces, and that the cohomology of a classifying space of a compact totally disconnected group is the Kan extension of the algebraic cohomology of a finite group.
6#
發(fā)表于 2025-3-22 14:52:32 | 只看該作者
Algebraic background, a graded commutative R-algebra. The natural inclusion map Hom(G, . Hom (∧ .,. then extends uniquely to a morphism of graded B-algebras ∧ Hom(G, . Horn (A ., . In order to familiarize ourselves with the situation, we will calculate explicitly this morphism. Similar considerations pertain to the case of . in place of ∧.
7#
發(fā)表于 2025-3-22 19:15:15 | 只看該作者
8#
發(fā)表于 2025-3-23 00:33:28 | 只看該作者
to their study: Analysis enters through the representation theory and harmonic analysis; differential geo- metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric stru
9#
發(fā)表于 2025-3-23 05:19:29 | 只看該作者
Levels and Tasks of Sentiment Analysisheory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again play a role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory.
10#
發(fā)表于 2025-3-23 06:15:44 | 只看該作者
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