Description
This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis”, dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics. This book provides comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry.
Contents
Preface
Contents
1. Global aspects of Finsler geometry (T. Aikou and L. Kozma)
2. Morse theory and nonlinear differential equations (T. Bartsch, A. Szulkin and M. Willem)
3. Index theory (D. Bleecker)
4. Partial differential equations on closed and open manifolds (J. Eichhorn)
5. Spectral geometry (P. Gilkey)
6. Lagrangian formalism on Grassmann manifolds (D.R. Grigore)
7. Sobolev spaces on manifolds (E. Hebey and F. Robert)
8. Harmonic maps (F. Heacute;lein and J.C. Wood)
9. Topology of differentiable mappings (K. Houston)
10. Group actions and Hilbert's fifth problem (S. Illman)
11. Exterior differential systems (N. Kamran)
12. Weil bundles as generalized jet spaces (I. Kolaacute;r)
13. Distributions, vector distributions, and immersions of manifolds in Euclidean spaces (J. Korbas)
14. Geometry of differential equations (B. Kruglikov and V. Lychagin)
15. Global variational theory in fibred spaces (D. Krupka)
16. Second Order Ordinary Differential Equations in Jet Bundles and the Inverse Problem of the Calculus of Variations (O. Krupkovaacute; and G.E. Prince)
17. Elements of noncommunicative geometry (G. Landi)
18. De Rham cohomology (M.A. Malakhaltsev)
19. Topology of manifolds with corners (J. Margalef-Roig and E. Outerelo Domiacute;nguez) 20. Jet manifolds and natural bundles (D.J. Saunders)
21. Some aspects of differential theories (J. Szilasi and R.L. Lovas)
22. Variational sequences (R. Vitolo)
23. The Oka-Grauert-Gromov principle for holomorphic bundles (P-M. Wong) A. Abstracts