Contents
Preface
Chapter 1. Metri c Space s
1.1. Legendr e o n hyperboli c geometr y
1.2. Metri c space s an d lengt h space s
1.3. Th e coars e perspectiv e o n metri c space s
1.4. Group s an d leave s
1.5. Tree s an d complexe s
1.6. Hyperboli c spac e
1.7. Nilpoten t example s Heisenber g grou p
Chapter 2 . Coars e Space s
2.1. Th e abstrac t notio n o f coarse structur e
2.2. Topologica l coars e structur e
2.3. Th e Higso n coron a
2.4. Metrizatio n o f coarse structure s
2.5. Hyperbolizatio n
Chapter 3 . Growt h an d amenabilit y
3.1. Bounde d geometr y
3.2. Growt h
3.3. Amenabl e space s
3.4. Example s o f amenable an d nonamenabl e space s
3.5. Amenabl e group s
3.6. F0lner' s Theore m
3.7. Amenabilit y an d analysi s
Chapter 4 . Translatio n Algebra s
4.1. Translatio n Algebra s
4.2. Amenabilit y an d th e Translatio n Algebr a
4.3. Finitenes s o f Grou p Algebra s
4.4. Translatio n C*-Algebra s
4.5. Translatio n Algebra s a s Crosse d Product s
Chapter 5 . Coars e Algebrai c Topolog y
5.1. Coars e cohomolog y theor y
5.2. Produc t structur e o n coars e theor y
5.3. Computatio n o f coarse cohomolog y
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