Connectivity properties of group actions on non-positively curved spaces / / Robert Bieri, Ross Geoghegan

• Record Nr.: UNINA9910480949703321
• Autore: Bieri Robert
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2003
• ISBN: 1-4704-0363-3
• Descrizione fisica: 1 online resource (105 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 765
• Disciplina: 510 s; 512/.2
• Soggetti: Geometric group theory; Connections (Mathematics); Global differential geometry; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "January 2003, volume 161, number 765 (second of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references (pages 81-83).
• Nota di contenuto: ""Contents""; ""Preface""; ""Chapter 1. Introduction""; ""1.1. Cocompact is an open condition""; ""1.2. Controlled connectivity""; ""1.3. The Boundary Criterion""; ""1.4. The Geometric Invariants""; ""Part 1. Controlled connectivity and openness results""; ""Chapter 2. Outline, Main Results and Examples""; ""2.1. Non-positively curved spaces""; ""2.2. Controlled connectivity: the definition of CC[sup(n-1)]""; ""2.3. The case of discrete orbits""; ""2.4. The Openness Theorem""; ""2.5. Connections with Lie groups and local rigidity""; ""2.6. The new tool""; ""2.7. Summary of the core idea""; ""2.8. SL[sup(2)] examples""""Chapter 3. Technicalities Concerning the CC[sup(n-1)]Property""; ""3.1. Local and global versions of CC[sup(n-1)]""; ""3.2. The Invariance Theorem""; ""Chapter 4. Finitary Maps and Sheaves of Maps""; ""4.1. Sheaves of maps""; ""4.2. G-sheaves""; ""4.3. Locally finite sheaves""; ""4.4. Embedding sheaves into homotopically closed sheaves""; ""4.5. Composing sheaves""; ""4.6. Homotopy of sheaves""; ""4.7. Finitary maps""; ""Chapter 5. Sheaves and Finitary Maps Over a Control Space""; ""5.1. Displacement function and norm""; ""5.2. Shift towards a point of M""; ""5.3. Contractions""""5.4. Guaranteed shift""; ""5.5. Defect of a sheaf""; ""Chapter 6. Construction of Sheaves with Positive Shift""; ""6.1. The case when dim X = 0""; ""6.2. Measuring the loss of guaranteed shift in an extension""; ""6.3. Imposing CAT(0)""; ""6.4. The main technical theorem""; ""Chapter 7. Controlled Connectivity as an Open Condition""; ""7.1. The topology on the set of all G-actions""; ""7.2. Continuous choice of control functions""; ""7.3. Imposing CAT(0)""; ""7.4. The Openness Theorem""; ""Chapter 8. Completion of the proofs of Theorems A and A'""; ""8.1. Controlled acyclicity""""8.2. The F[sub(n)] Criterion""; ""8.3. Proof of Theorem A""; ""8.4. Properly discontinuous actions""; ""Chapter 9. The Invariance Theorem""; ""Part 2. The geometric invariants""; ""Short summary of Part 2""; ""Chapter 10. Outline, Main Results and Examples""; ""10.1. The boundary of a CAT(0)-space""; ""10.2. CC[sup(n-1)] over end points""; ""10.3. The dynamical subset""; ""10.4. Openness results""; ""10.5. Endpoints versus points in M""; ""10.6. Fixed points and the BNSR-geometric invariant""; ""10.7. Examples""; ""Chapter 14. From CC[sup(n-1)] over Endpoints to Contractions""