04229nam 2200637 450 991081910100332120170822144132.01-4704-0506-7(CKB)3360000000465084(EBL)3114095(SSID)ssj0000888885(PQKBManifestationID)11539773(PQKBTitleCode)TC0000888885(PQKBWorkID)10874445(PQKB)10167324(MiAaPQ)EBC3114095(RPAM)15072333(PPN)195417895(EXLCZ)99336000000046508420071106h20082008 uy| 0engur|n|---|||||txtccrDifferential geometry, Lie groups, and symmetric spaces over general base fields and rings /Wolfgang BertramProvidence, Rhode Island :American Mathematical Society,[2008]©20081 online resource (218 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 900Description based upon print version of record.0-8218-4091-6 Includes bibliographical references (pages 199-202).""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""""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""""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""""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""Memoirs of the American Mathematical Society ;no. 900.Infinite dimensional Lie algebrasInfinite-dimensional manifoldsSymmetric spacesGeometry, DifferentialInfinite dimensional Lie algebras.Infinite-dimensional manifolds.Symmetric spaces.Geometry, Differential.510 s512/.482Bertram Wolfgang1965-65496MiAaPQMiAaPQMiAaPQBOOK9910819101003321Differential geometry, Lie groups, and symmetric spaces over general base fields and rings3948169UNINA