LEADER 03675nam 2200613 450 001 9910788749803321 005 20170822144505.0 010 $a1-4704-0436-2 035 $a(CKB)3360000000465019 035 $a(EBL)3114252 035 $a(SSID)ssj0000973209 035 $a(PQKBManifestationID)11539950 035 $a(PQKBTitleCode)TC0000973209 035 $a(PQKBWorkID)10958883 035 $a(PQKB)10349562 035 $a(MiAaPQ)EBC3114252 035 $a(RPAM)13946979 035 $a(PPN)195417232 035 $a(EXLCZ)993360000000465019 100 $a20050429h20052005 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHigher complex torsion and the framing principle /$fKiyoshi Igusa 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2005] 210 4$dİ2005 215 $a1 online resource (114 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 835 300 $a"Volume 177, number 835 (third of 4 numbers)." 311 $a0-8218-3773-7 320 $aIncludes bibliographical references. 327 $a""Contents""; ""Introduction""; ""0.1. Higher Franz-Reidemeister torsion""; ""0.2. Construction of I??[sub(k)]""; ""0.3. Framing Principle""; ""0.4. Complex torsion""; ""Chapter 1. Complex torsion""; ""1.1. Definition for closed AC fibers""; ""1.2. Generalized Miller-Morita-Mumford classes""; ""1.3. Complex Framing Principle""; ""1.4. Nonempty boundary case""; ""Chapter 2. Definition of higher FRa???torsion""; ""2.1. Generalized Morse functions""; ""2.2. Families of chain complexes""; ""2.3. Monomial functors""; ""2.4. Filtered chain complexes""; ""2.5. Subfunctors"" 327 $a""2.6. The Whitehead category""""2.7. Definition in acyclic case""; ""2.8. Families of matrices as flat superconnections""; ""2.9. Independence of birth-death points""; ""2.10. Positive suspension lemma""; ""2.11. Definition in upper triangular case""; ""Chapter 3. Properties of higher FRa???torsion""; ""3.1. Basic properties""; ""3.2. Suspension Theorem""; ""3.3. Additivity, Splitting Lemma""; ""3.4. Applications of the Splitting Lemma""; ""3.5. Local equivalence lemma""; ""3.6. Product formula""; ""3.7. Transfer for coverings""; ""3.8. More transfer formulas"" 327 $a""Chapter 4. The Framing Principle""""4.1. Statement for Morse bundles""; ""4.2. General statement""; ""4.3. Push-down/transfer""; ""4.4. The Framing Principle""; ""Chapter 5. Proof of the Framing Principle""; ""5.1. Transfer theorem""; ""5.2. Stratified deformation lemma""; ""5.3. Proof of transfer theorem""; ""5.4. Proof of Framing Principle""; ""Chapter 6. Applications of the Framing Principle""; ""6.1. Torelli group""; ""6.2. Even dimensional fibers""; ""6.3. Unoriented fibers""; ""6.4. Vertical normal disk bundle""; ""Chapter 7. The Stability Theorem""; ""7.1. Definitions"" 327 $a""7.2. Stability for C(M)""""7.3. Involution""; ""7.4. Disks and spheres""; ""7.5. Relation to higher torsion""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 835. 606 $aReidemeister torsion 606 $aDifferentiable mappings 606 $aDiffeomorphisms 615 0$aReidemeister torsion. 615 0$aDifferentiable mappings. 615 0$aDiffeomorphisms. 676 $a510 s 676 $a514/.72 700 $aIgusa$b Kiyoshi$f1949-$01521052 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788749803321 996 $aHigher complex torsion and the framing principle$93759923 997 $aUNINA