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
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