作者简介 鲍里斯•杜布罗文(B. A. Dubrovin)、阿纳托利•福缅科(A. T. Fomenko)和谢尔盖•诺维科夫(S. P. Novikov)都是苏联/俄罗斯有名数学家,三位数学家都毕业于莫斯科大学,并在莫斯科大学任教。杜布罗文在苏联解体后去了意大利国际高等研究院任教,在他2019年去世后,意大利国际高等研究院在莫斯科数学会等组织的支持下设立了杜布罗文奖章,授予那些在数学物理和几何领域做出突出贡献的青年数学家,每两年颁奖一次。福缅科和诺维科夫都是俄罗斯科学院院士,福缅科获得过1996年俄罗斯联邦国家奖,诺维科夫获得过1970年菲尔兹奖和2005年沃尔夫奖。
目录 Preface. Chapter 1: Examples of Manifolds. Chapter 2: Foundational Questions. Essential Facts Concerning Functions on a Manifold. Typical Smooth Mappings. Chapter 3: The Degree of a Mapping. The Intersection Index of Submanifolds. Applications. Chapter 4: Orientability of Manifolds. The Fundamental Group. Covering Spaces (Fibre Bundles with Discrete Fibre). Chapter 5: Homotopy Groups. Chapter 6: Smooth Fibre Bundles. Chapter 7: Some Examples of Dynamical Systems and Foliations on Manifolds. Chapter 8: The Global Structure of Solutions of Higher-Dimensional Variational Problems. Bibliography.
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