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Titlebook: Metric Structures for Riemannian and Non-Riemannian Spaces; Mikhail Gromov Book 2007 Birkh?user Boston 2007 Algebraic topology.Homotopy.Ma

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書目名稱Metric Structures for Riemannian and Non-Riemannian Spaces
編輯Mikhail Gromov
視頻videohttp://file.papertrans.cn/633/632469/632469.mp4
叢書名稱Modern Birkh?user Classics
圖書封面Titlebook: Metric Structures for Riemannian and Non-Riemannian Spaces;  Mikhail Gromov Book 2007 Birkh?user Boston 2007 Algebraic topology.Homotopy.Ma
描述.Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory...The new wave began with seminal papers by Svarc and Milnor on the growth of groups and the spectacular proof of the rigidity of lattices by Mostow. This progress was followed by the creation of the asymptotic metric theory of infinite groups by Gromov...The structural metric approach to the Riemannian category, tracing back to Cheeger‘s thesis, pivots around the notion of the Gromov–Hausdorff distance between Riemannian manifolds. This distance organizes Riemannian manifolds of all possible topological types into a single connected moduli space, where convergence allows the collapse of dimension with unexpectedly rich geometry, as revealed in the work of Cheeger, Fukaya, Gromov and Perelman. Also, Gromov found metric structure within homotopy theory and thus introduced new invariants controlling combinatorial complexity of maps and spaces, such as the simplicial volume, which is responsible for degrees of maps between manifolds. During the same
出版日期Book 2007
關(guān)鍵詞Algebraic topology; Homotopy; Mathematics; Probability theory; Riemannian geometry; Structures; Systole; Vo
版次1
doihttps://doi.org/10.1007/978-0-8176-4583-0
isbn_softcover978-0-8176-4582-3
isbn_ebook978-0-8176-4583-0Series ISSN 2197-1803 Series E-ISSN 2197-1811
issn_series 2197-1803
copyrightBirkh?user Boston 2007
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Length Structures: Path Metric Spaces,introduce the fundamental notions of covariant derivative and curvature (cf. [Grl-Kl-Mey] or [Milnor], Ch. 2), use is made only of the differentiability of . and not of its positivity, as illustrated by Lorentzian geometry in general relativity. By contrast, the concepts of the length of curves in .
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Morse Theory and Minimal Models,bounded by a disk of area at most .. This definition only makes sense in noncompact manifolds, and we have shown that the 2-dimensional isoperimetric rank of the universal cover of a compact manifold . depends only on the fundamental group .(.).
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