| 书目名称 | Metric Structures for Riemannian and Non-Riemannian Spaces | | 编辑 | Mikhail Gromov | | 视频video | | | 丛书名称 | Modern Birkhäuser Classics | | 图书封面 |  | | 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 | | 关键词 | Algebraic topology; Homotopy; Mathematics; Probability theory; Riemannian geometry; Structures; Systole; Vo | | 版次 | 1 | | doi | https://doi.org/10.1007/978-0-8176-4583-0 | | isbn_softcover | 978-0-8176-4582-3 | | isbn_ebook | 978-0-8176-4583-0Series ISSN 2197-1803 Series E-ISSN 2197-1811 | | issn_series | 2197-1803 | | copyright | Birkhäuser Boston 2007 |
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发表于 2025-3-21 16:41:44
