04338nam 2200625 450 991080703810332120180613001303.01-4704-0363-3(CKB)3360000000464949(EBL)3114352(SSID)ssj0000973337(PQKBManifestationID)11539959(PQKBTitleCode)TC0000973337(PQKBWorkID)10958541(PQKB)10889775(MiAaPQ)EBC3114352(RPAM)12899185(PPN)195416511(EXLCZ)99336000000046494920020819d2003 uy| 0engur|n|---|||||txtccrConnectivity properties of group actions on non-positively curved spaces /Robert Bieri, Ross GeogheganProvidence, Rhode Island :American Mathematical Society,2003.1 online resource (105 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 765"January 2003, volume 161, number 765 (second of 5 numbers)."0-8218-3184-4 Includes bibliographical references (pages 81-83).""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""Memoirs of the American Mathematical Society ;no. 765.Geometric group theoryConnections (Mathematics)Global differential geometryGeometric group theory.Connections (Mathematics)Global differential geometry.510 s512/.2Bieri Robert1608765Geoghegan Ross1963-MiAaPQMiAaPQMiAaPQBOOK9910807038103321Connectivity properties of group actions on non-positively curved spaces3935681UNINA