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內詣零流形映射的尼爾森數的阿諾索夫關系:英文 版權信息
- ISBN：9787576706093
- 條形碼：9787576706093 ; 978-7-5767-0609-3
- 裝幀：平裝-膠訂
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
內詣零流形映射的尼爾森數的阿諾索夫關系:英文 內容簡介
本書分為三個部分，**部分內容驗證了內諧零流形M的（連續）自映射f：M→M的阿諾索夫關系，回顧了內詣零流形的主要性質和定義，還展示了內詣零流形與可解流形是不同的；第二部分內容給出了有兩種可能的方式去推廣阿諾索夫定理，**種方式是尋找流形類，而不是詣零流形，這就使該關系對已知流形的所有連續映射都成立；第三部分內容集中討論了低維內詣流形，也就是4維內詣流形，幾乎為每個比伯巴赫群提供了特殊比伯巴赫群（或內詣零流形）的阿諾索夫關系的證明或反例。
內詣零流形映射的尼爾森數的阿諾索夫關系:英文 目錄
Preface
Part I Preliminaries
1 Maps of infra-nilmanifolds: an algebraic description
1.1 Lie groups
1.2 Infra-nilmanifolds
1.3 Maps of infra-nilmanifolds
2 The Anosov relation
2.1 Fixed point theory
2.1.1 The Lefschetz number
2.1.2 The Nielsen number
2.1.3 The Anosov relation
2.2 Fixed point theory on infra-nilmanifolds
Part II The results
3 Periodic sequences and infra-nilmanifolds with an odd order holonomy group
3.1 The Anosov theorem for infra-nilmanifolds with odd order holonomy group
3.2 Classes of maps for which the Anosov theorem hold
3.2.1 The Anosov relation for expanding maps
3.2.2 The Anosov relation for nowhere expanding maps
3.3 Infra-nilmanifolds are more complicated
4 Anosov diffeomorphisms
4.1 Algebraic characterization
4.2 Non-primitive fiat manifolds
4.2.1 Flat n-dinensional manifolds with first Betti number smaller than n - 2
4.2.2 Flat manifolds with first Betti number equal to n - 2
4.3 Primitive fiat manifolds
4.3.1 Primitive fiat manifolds in dimension n ) 6
4.3.2 Primitive fiat manifolds in dimension 6
5 Infra-nilmanifolds with cyclic holonomy group
5.1 Cyclic groups of matrices
5.2 The Anosov theorem for infra-nilmanifolds with cyclic holonomy group
5.3 The sharpness of the main result for fiat manifolds
6 Generalized Hantzsche-Wendt manifolds
6.1 Definition and properties
6.2 Orientable fiat GHW manifolds
Part III The Anosov theorem in small dimensions
7 Flat manifolds
7.1 General overview in dimension 3 and 4
7.2 Flat manifolds in dimension 4 with Z2 Z2 as holonomy group
7.3 Flat manifolds in dimension 4 with non-abelian holonomy group
8 Infra-nilmanifolds
8.1 Calculations on 4 dimensional infra-nilmanifolds
8.1.1 2-step nilpotent infra-nilmanifolds
8.1.2 3-step nilpotent infra-nilmanifolds
8.2 The 3-dimensional, 2-step infra-nilmanifolds
8.3 The 4-dimensional, 2-step infra-nilmanifolds
8.3.1 Abelian holonomy group
8.3.2 Non-abelian holonomy group
8.4 The 4-dimensional, 3-step infra-nilmanifolds
References
編輯手記
Part I Preliminaries
1 Maps of infra-nilmanifolds: an algebraic description
1.1 Lie groups
1.2 Infra-nilmanifolds
1.3 Maps of infra-nilmanifolds
2 The Anosov relation
2.1 Fixed point theory
2.1.1 The Lefschetz number
2.1.2 The Nielsen number
2.1.3 The Anosov relation
2.2 Fixed point theory on infra-nilmanifolds
Part II The results
3 Periodic sequences and infra-nilmanifolds with an odd order holonomy group
3.1 The Anosov theorem for infra-nilmanifolds with odd order holonomy group
3.2 Classes of maps for which the Anosov theorem hold
3.2.1 The Anosov relation for expanding maps
3.2.2 The Anosov relation for nowhere expanding maps
3.3 Infra-nilmanifolds are more complicated
4 Anosov diffeomorphisms
4.1 Algebraic characterization
4.2 Non-primitive fiat manifolds
4.2.1 Flat n-dinensional manifolds with first Betti number smaller than n - 2
4.2.2 Flat manifolds with first Betti number equal to n - 2
4.3 Primitive fiat manifolds
4.3.1 Primitive fiat manifolds in dimension n ) 6
4.3.2 Primitive fiat manifolds in dimension 6
5 Infra-nilmanifolds with cyclic holonomy group
5.1 Cyclic groups of matrices
5.2 The Anosov theorem for infra-nilmanifolds with cyclic holonomy group
5.3 The sharpness of the main result for fiat manifolds
6 Generalized Hantzsche-Wendt manifolds
6.1 Definition and properties
6.2 Orientable fiat GHW manifolds
Part III The Anosov theorem in small dimensions
7 Flat manifolds
7.1 General overview in dimension 3 and 4
7.2 Flat manifolds in dimension 4 with Z2 Z2 as holonomy group
7.3 Flat manifolds in dimension 4 with non-abelian holonomy group
8 Infra-nilmanifolds
8.1 Calculations on 4 dimensional infra-nilmanifolds
8.1.1 2-step nilpotent infra-nilmanifolds
8.1.2 3-step nilpotent infra-nilmanifolds
8.2 The 3-dimensional, 2-step infra-nilmanifolds
8.3 The 4-dimensional, 2-step infra-nilmanifolds
8.3.1 Abelian holonomy group
8.3.2 Non-abelian holonomy group
8.4 The 4-dimensional, 3-step infra-nilmanifolds
References
編輯手記
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