00000007.htm

viii CONTENTS

bundles. 3. Currents and distributions. 4. Local definition of a current. Support
of a current. 5. Currents on an oriented manifold. Distributions on R". 6. Real
distributions. Positive distributions. 7. Distributions with compact support.
Point-distributions. 8. The weak topology on spaces of distributions. 9. Ex-
ample: finite parts of divergent integrals, 10. Tensor products of distributions.
11. Convolution of distributions on a Lie group. 12. Regularization of distribu-
tions. 13. Differential operators and fields of point-distributions. 14. Vector
fields as differential operators. 15. The exterior differential of a differential p-
form. 16. Connections in a vector bundle. 17. Differential operators associated
with a connection. 18. Connections on a differential manifold. 19. The covariant
exterior differential. 20. Curvature and torsion of a connection.

Appendix

MULTILINEAR ALGEBRA.......................347

8. Modules. Free modules. 9. Duality for free modules. 10. Tensor product of
free modules. 11. Tensors. 12. Symmetric and antisymmetric tensors. 13.
The exterior algebra. 14. Duality in the exterior algebra. 15. Interior products.
16. Nondegenerate alternating bilinear forms. Symplectic groups. 17. The sym-
metric algebra. 18. Derivations and antiderivations of graded algebras. 19.
Lie algebras.

References.................................378

Index...................................381



	viii CONTENTS bundles. 3. Currents and distributions. 4. Local definition of a current. Support of a current. 5. Currents on an oriented manifold. Distributions on R". 6. Real distributions. Positive distributions. 7. Distributions with compact support. Point-distributions. 8. The weak topology on spaces of distributions. 9. Ex- ample: finite parts of divergent integrals, 10. Tensor products of distributions. 11. Convolution of distributions on a Lie group. 12. Regularization of distribu- tions. 13. Differential operators and fields of point-distributions. 14. Vector fields as differential operators. 15. The exterior differential of a differential p- form. 16. Connections in a vector bundle. 17. Differential operators associated with a connection. 18. Connections on a differential manifold. 19. The covariant exterior differential. 20. Curvature and torsion of a connection. Appendix MULTILINEAR ALGEBRA.......................347 8. Modules. Free modules. 9. Duality for free modules. 10. Tensor product of free modules. 11. Tensors. 12. Symmetric and antisymmetric tensors. 13. The exterior algebra. 14. Duality in the exterior algebra. 15. Interior products. 16. Nondegenerate alternating bilinear forms. Symplectic groups. 17. The sym- metric algebra. 18. Derivations and antiderivations of graded algebras. 19. Lie algebras. References.................................378 Index...................................381