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Titlebook: Basic Concepts of Synthetic Differential Geometry; René Lavendhomme Book 1996 Springer Science+Business Media Dordrecht 1996 Lie group.alg

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發(fā)表于 2025-3-21 17:54:43 | 只看該作者 |倒序瀏覽 |閱讀模式
期刊全稱Basic Concepts of Synthetic Differential Geometry
影響因子2023René Lavendhomme
視頻videohttp://file.papertrans.cn/181/180993/180993.mp4
學(xué)科分類Texts in the Mathematical Sciences
圖書封面Titlebook: Basic Concepts of Synthetic Differential Geometry;  René Lavendhomme Book 1996 Springer Science+Business Media Dordrecht 1996 Lie group.alg
影響因子Starting at an introductory level, the book leads rapidly toimportant and often new results in synthetic differential geometry.From rudimentary analysis the book moves to such important results as:a new proof of De Rham‘s theorem; the synthetic view of global action,going as far as the Weil characteristic homomorphism; the systematicaccount of structured Lie objects, such as Riemannian, symplectic, orPoisson Lie objects; the view of global Lie algebras as Lie algebrasof a Lie group in the synthetic sense; and lastly the syntheticconstruction of symplectic structure on the cotangent bundle ingeneral. Thus while the book is limited to a naive point of viewdeveloping synthetic differential geometry as a theory in itself, theauthor nevertheless treats somewhat advanced topics, which are classicin classical differential geometry but new in the synthetic context...Audience:. The book is suitable as an introduction to syntheticdifferential geometry for students as well as more qualifiedmathematicians.
Pindex Book 1996
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https://doi.org/10.1007/978-981-19-8803-5We encountered in 1.1 various small objects, the most typical and simple one being .. We intend to indicate in this section a more algebraic view of these small objects.
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Der erste Nachweis der KernspaltungAn important problem in differential geometry is how one can compare tangent vectors at one point to those at another, at least in the case of nearby points. We ask if, at least during an infinitesimal period of time, it is possible to “transport” a tangent vector in the direction of another tangent vector.
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https://doi.org/10.1007/978-3-322-84225-1First we define the fundamental concept of Riemannian structure. We must clarify the notion of non-degenerate map, because, in our logic, the function of negation is tricky.
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Connections,An important problem in differential geometry is how one can compare tangent vectors at one point to those at another, at least in the case of nearby points. We ask if, at least during an infinitesimal period of time, it is possible to “transport” a tangent vector in the direction of another tangent vector.
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