An Introduction to Differential Manifolds

Dennis Barden, Charles B Thomas

  • 出版商: Imperial College Pre
  • 出版日期: 2003-03-13
  • 售價: $1,950
  • 貴賓價: 9.5$1,853
  • 語言: 英文
  • 頁數: 232
  • 裝訂: Paperback
  • ISBN: 1860943551
  • ISBN-13: 9781860943553
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This invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology. Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups using differential forms (de Rham theory), and applications such as the Poincaré-Hopf theorem relating the Euler number of a manifold and the index of a vector field. Each chapter contains exercises of varying difficulty for which solutions are provided. Special features include examples drawn from geometric manifolds in dimension 3 and Brieskorn varieties in dimensions 5 and 7, as well as detailed calculations for the cohomology groups of spheres and tori.


這本寶貴的書籍基於兩位作者多年的教學經驗,向讀者介紹微分拓撲的基本概念。其中涵蓋的主題包括光滑流形和映射、切線丛及其相關結構、使用微分形式(de Rham 理論)計算實值上同調群,以及應用,如庞加莱-霍普夫定理關聯流形的歐拉數和向量場的指數。每章包含不同難度的練習題,並提供解答。特色包括從三維幾何流形和五維、七維的 Brieskorn 變種中選取的例子,以及球面和鈴形曲面上同調群的詳細計算。