网站首页 软件下载 游戏下载 翻译软件 电子书下载 电影下载 电视剧下载 教程攻略
书名 | 现代几何学--方法和应用(第3卷同调论导论英文版)(精)/俄罗斯数学经典 |
分类 | 科学技术-自然科学-数学 |
作者 | (俄罗斯)鲍里斯·杜布罗文//阿纳托利·福缅科//谢尔盖·诺维科夫 |
出版社 | 世界图书出版公司 |
下载 | |
简介 | 内容推荐 本书是莫斯科大学数学力学系经典教材《现代几何学——方法和应用》三卷本的第3卷。全书力求以直观的和物理的视角阐述,是一本难得的现代几何方面的佳作。整套书内容包括张量分析、曲线和曲面几何、一维和高维变分法(第1卷),微分流形的拓扑和几何(第2卷),以及同调与上同调理论(第3卷)。本书可用作数学和理论物理专业高年级和研究生的教学用书,对从事几何和拓扑研究的工作者也极具参考价值。 目录 Preface CHAPTER 1 Homology and Cohomology. Computational Recipes 1. Cohomology groups as classes of closed differential forms. Their homotopy invariance 2. The homology theory of algebraic complexes 3. Simplicial complexes. Their homology and cohomology groups. The classification of the two-dimensional closed surfaces 4. Attaching cells to a topological space. Cell spaces. Theorems on the reduction of cell spaces. Homology groups and the fundamental groups of surfaces and certain other manifolds 5. The singular homology and cohomology groups. Their homotogy invariance. The exact sequence of a pair. Relative homology groups 6. The singular homology of cell complexes. Its equivalence with cell homology. Poincare duality in simplicial homology 7. The homology groups of a product of spaces. Multiplication in cohomology rings. The cohomology theory of H-spaces and Lie groups. The cohomology of the unitary groups 8. The homology theory of fibre bundles (skew products) 9. The extension problem for maps, homotopies, and cross-sections. Obstruction cohomology classes 9.1. The extension problem for maps 9.2. The extension problem for homotopies 9.3. The extension problem for cross-sections 10. Homology theory and methods for computing homotopy groups. The Cartan-Serre theorem. Cohomology operations. Vector bundles. 10.1. The concept of a cohomology operation. Examples 10.2. Cohomology operations and Eilenberg-MacLane complexes 10.3. Computation of the rational homotopy groups πi □(特殊字符) 10.4. Application to vector bundles. Characterist ic classes 10.5. Classification of the Steenrod operations in low dimensions 10.6. Computation of the first few nontrivial stable homotopy groups of spheres 10.7. Stable homotopy classes of maps of cell complexes 11. Homology theory and the fundamental group 12. The cohomology groups of hyperelliptic Riemann surfaces. Jacobi tori. Geodesics on multi-axis ellipsoids, Relationship to finite-gap potentials 13. The simplest properties of Kihler manifolds. Abelian tori 14. Sheaf cohomology CHAPTER 2 Critical Points of Smooth Functions and Homology Theory 15. Morse functions and cell complexes 16. The Morse inequalities 17. Morse-Smale functions. Handles. Surfaces 18. Poinoare duality 19. Critical points of smooth functions and the Lyusternik- Shnirelman category of a manifold 20. Critical manifolds and the Morse inequalities. Fuactions with symmetry 21. Critical points of functionals and the topology of the path space Ω(M) 22. Applications of the index theorem 23. The periodic problem of the calculus of variation 24. Morse functions on 3-dimensional manifolds and Heegaard splittings 25. Unitary Bott periodicity and higher-dimensional variational problems 25.1. The theorem on unitary periodicity 25.2. Unitary periodicity via the two-dimensiona, calculus of variations 25.3. Onthogonal periodicity via the higher-dime asional calculus of variations 26. Morse theory and certain motions in the planar n-body problem CHAPTER 3 Cobordisms and Smooth Structures 27. Characteristic numbers. Cobordisms. Cycles and submanifolds. The signature of a manifold 27.1. Statement of the problem. The simplest fact,; about cobordisms, The signature 27.2. Thorn complexes. Calculation of cobordisms (modulo torsion). The signature formula. Realization of cycles as submanifolds 27.3. Some applications of the signature formula. The signature and the problem of the invariance of classes 28. Smooth structures on the 7-dimensional sphere. The classification problem for smooth manifolds (normal invariants). Reidemeister torsion and the fundamental hypothesis (Hauptvermutung) of combinatorial topology Bibliography APPENDIX 1 (by S. P. Novikov) An Analogue of Morse Theory for Many-Valued Functions. Cer |
随便看 |
|
霍普软件下载网电子书栏目提供海量电子书在线免费阅读及下载。