| 书目名称 | Topological Crystallography | | 副标题 | With a View Towards | | 编辑 | Toshikazu Sunada | | 视频video | | | 概述 | Useful for both mathematicians and practical scientists, who know how ideas developed in pure mathematics are applied to a practical problem.Designed to be as self-contained as possible, so that the r | | 丛书名称 | Surveys and Tutorials in the Applied Mathematical Sciences | | 图书封面 |  | | 描述 | .Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s .Elements.. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. .This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title .Topological Crystallography. has been chosen..Topological crystals can be described as “living in the logical world, not in space,” | | 出版日期 | Book 2013 | | 关键词 | Covering map; Discrete Abel--Jacobi map; Homology group; Standard realization; Topological crystal | | 版次 | 1 | | doi | https://doi.org/10.1007/978-4-431-54177-6 | | isbn_softcover | 978-4-431-54176-9 | | isbn_ebook | 978-4-431-54177-6Series ISSN 2199-4765 Series E-ISSN 2199-4773 | | issn_series | 2199-4765 | | copyright | Springer Japan 2013 |
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发表于 2025-3-21 16:38:49
