LEADER 04229nam 2200637 450 001 9910819101003321 005 20170822144132.0 010 $a1-4704-0506-7 035 $a(CKB)3360000000465084 035 $a(EBL)3114095 035 $a(SSID)ssj0000888885 035 $a(PQKBManifestationID)11539773 035 $a(PQKBTitleCode)TC0000888885 035 $a(PQKBWorkID)10874445 035 $a(PQKB)10167324 035 $a(MiAaPQ)EBC3114095 035 $a(RPAM)15072333 035 $a(PPN)195417895 035 $a(EXLCZ)993360000000465084 100 $a20071106h20082008 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDifferential geometry, Lie groups, and symmetric spaces over general base fields and rings /$fWolfgang Bertram 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2008] 210 4$dİ2008 215 $a1 online resource (218 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 900 300 $aDescription based upon print version of record. 311 $a0-8218-4091-6 320 $aIncludes bibliographical references (pages 199-202). 327 $a""Contents""; ""Introduction""; ""I. Basic notions""; ""1. Differential calculus""; ""2. Manifolds""; ""3. Tangent bundle and general fiber bundles""; ""4. The Lie bracket of vector fields""; ""5. Lie groups and symmetric spaces: basic facts""; ""II. Interpretation of tangent objects via scalar extensions""; ""6. Scalar extensions. I: Tangent functor and dual numbers""; ""7. Scalar extensions. II: Higher order tangent functors""; ""8. Scalar extensions. Ill: Jet functor and truncated polynomial rings""; ""III. Second order differential geometry"" 327 $a""9. The structure of the tangent bundle of a vector bundle""""10. Linear connections. I: Linear structures on bilinear bundles""; ""11. Linear connections. II: Sprays""; ""12. Linear connections. Ill: Covariant derivative""; ""13. Natural operations. I: Exterior derivative of a one-form""; ""14. Natural operations. II: The Lie bracket revisited""; ""IV. Third and higher order differential geometry""; ""15. The structure of T[sup(k)]F: Multilinear bundles""; ""16. The structure of T[sup(k)]F: Multilinear connections""; ""17. Construction of multilinear connections""; ""18. Curvature"" 327 $a""19. Linear structures on jet bundles""""20. Shifts and symmetrization""; ""21. Remarks on differential operators and symbols""; ""22. The exterior derivative""; ""V. Lie Theory""; ""23. The three canonical connections of a Lie group""; ""24. The structure of higher order tangent groups""; ""25. Exponential map and Campbell-Hausdorff formula""; ""26. The canonical connection of a symmetric space""; ""27. The higher order tangent structure of symmetric spaces""; ""VI.Diffeomorphism Groups and the exponential jet""; ""28. Group structure on the space of sections of T[sup(k)]M"" 327 $a""29. The exponential jet for vector fields""""30. The exponential jet of a symmetric space""; ""31. Remarks on the exponential jet of a general connection""; ""32. From germs to jets and from jets to germs""; ""Appendix L. Limitations""; ""Appendix G. Generalizations""; ""Appendix: Multilinear Geometry""; ""BA. Bilinear algebra""; ""MA. Multilinear algebra""; ""SA. Symmetric and shift invariant multilinear algebra""; ""PG. Polynomial groups""; ""References"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 900. 606 $aInfinite dimensional Lie algebras 606 $aInfinite-dimensional manifolds 606 $aSymmetric spaces 606 $aGeometry, Differential 615 0$aInfinite dimensional Lie algebras. 615 0$aInfinite-dimensional manifolds. 615 0$aSymmetric spaces. 615 0$aGeometry, Differential. 676 $a510 s 676 $a512/.482 700 $aBertram$b Wolfgang$f1965-$065496 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910819101003321 996 $aDifferential geometry, Lie groups, and symmetric spaces over general base fields and rings$93948169 997 $aUNINA