LEADER 04338nam 2200625 450 001 9910807038103321 005 20180613001303.0 010 $a1-4704-0363-3 035 $a(CKB)3360000000464949 035 $a(EBL)3114352 035 $a(SSID)ssj0000973337 035 $a(PQKBManifestationID)11539959 035 $a(PQKBTitleCode)TC0000973337 035 $a(PQKBWorkID)10958541 035 $a(PQKB)10889775 035 $a(MiAaPQ)EBC3114352 035 $a(RPAM)12899185 035 $a(PPN)195416511 035 $a(EXLCZ)993360000000464949 100 $a20020819d2003 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aConnectivity properties of group actions on non-positively curved spaces /$fRobert Bieri, Ross Geoghegan 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2003. 215 $a1 online resource (105 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 765 300 $a"January 2003, volume 161, number 765 (second of 5 numbers)." 311 $a0-8218-3184-4 320 $aIncludes bibliographical references (pages 81-83). 327 $a""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"" 327 $a""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"" 327 $a""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'"" 327 $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"" 327 $a""Chapter 14. From CC[sup(n-1)] over Endpoints to Contractions"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 765. 606 $aGeometric group theory 606 $aConnections (Mathematics) 606 $aGlobal differential geometry 615 0$aGeometric group theory. 615 0$aConnections (Mathematics) 615 0$aGlobal differential geometry. 676 $a510 s 676 $a512/.2 700 $aBieri$b Robert$01608765 702 $aGeoghegan$b Ross$f1963- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910807038103321 996 $aConnectivity properties of group actions on non-positively curved spaces$93935681 997 $aUNINA