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Titlebook: Geometry of Vector Sheaves; An Axiomatic Approac Anastasios Mallios Book 1998 Springer Science+Business Media Dordrecht 1998 Algebraic topo

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發(fā)表于 2025-3-21 20:00:56 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Geometry of Vector Sheaves
副標(biāo)題An Axiomatic Approac
編輯Anastasios Mallios
視頻videohttp://file.papertrans.cn/384/383833/383833.mp4
叢書名稱Mathematics and Its Applications
圖書封面Titlebook: Geometry of Vector Sheaves; An Axiomatic Approac Anastasios Mallios Book 1998 Springer Science+Business Media Dordrecht 1998 Algebraic topo
描述This two-volume monograph obtains fundamental notions andresults of the standard differential geometry of smooth(C.INFINITY.) manifolds, without using differentialcalculus. Here, the sheaf-theoretic character is emphasised. This hastheoretical advantages such as greater perspective, clarity andunification, but also practical benefits ranging from elementaryparticle physics, via gauge theories and theoretical cosmology(`differential spaces‘), to non-linear PDEs (generalised functions).Thus, more general applications, which are no longer `smooth‘ in theclassical sense, can be coped with. The treatise might also beconstrued as a new systematic endeavour to confront theever-increasing notion that the `world around us is far from beingsmooth enough‘. ..Audience:. This work is intended for postgraduate students andresearchers whose work involves differential geometry, globalanalysis, analysis on manifolds, algebraic topology, sheaf theory,cohomology, functional analysis or abstract harmonic analysis.
出版日期Book 1998
關(guān)鍵詞Algebraic topology; Characteristic class; abstract harmonic analysis; cohomology; curvature; differential
版次1
doihttps://doi.org/10.1007/978-94-011-5006-4
isbn_softcover978-94-010-6102-5
isbn_ebook978-94-011-5006-4
copyrightSpringer Science+Business Media Dordrecht 1998
The information of publication is updating

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沙發(fā)
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地板
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5#
發(fā)表于 2025-3-22 08:53:25 | 只看該作者
Classical Theory which the framework, exhibited hitherto in the preceding Chapters, constitutes their abstract (axiomatic) description. Of course, this happens in the . case, while certain . also are fitted in well, within the same context, as in the foregoing. A particularly interesting case is that one of the so-
6#
發(fā)表于 2025-3-22 13:08:40 | 只看該作者
Sheaves and presheaves with topological algebraic structuresposed in the preceding chapter, certain types of . too furnish further non-trivial examples, where one can apply the point of view of the present treatment, getting thus a considerable part of the standard machinery of the classical differential geometry. In this context, we still notice that, here
7#
發(fā)表于 2025-3-22 21:03:16 | 只看該作者
https://doi.org/10.1007/978-3-322-98685-6ed the . of the notion of an .-connection. As we shall presently see, several standard results of the classical .-manifolds are still in force, within the present abstract (axiomatic) framework. This means, at least, that . . (notwithstanding, its ., yes!) . . for the results in question.
8#
發(fā)表于 2025-3-23 01:04:51 | 只看該作者
-connections. Local Theoryed the . of the notion of an .-connection. As we shall presently see, several standard results of the classical .-manifolds are still in force, within the present abstract (axiomatic) framework. This means, at least, that . . (notwithstanding, its ., yes!) . . for the results in question.
9#
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10#
發(fā)表于 2025-3-23 06:27:14 | 只看該作者
https://doi.org/10.1007/978-3-642-75574-3is that . for this .; that is, . is involved at all(!), our tools being just ., in particular, . . (linear and multilinear) and/or ., to the extent that these issues have been developed in the preceding chapters. Nontheless, as we shall realize through the succeeding discussion, several fundamental
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