Morse theory |
ter |
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Teaching Staff in Charge |
Assoc.Prof. VARGA Csaba Gyorgy, Ph.D., csvarga@cs.ubbcluj.ro |
Aims |
The course gives the principal mathematical instrument in the study of infinite dimensional manifolds. The following topics are covered: infinite dimensional manifolds, imersions, submersions, transversality, theorems of Ereshmann, Morse and Gromoll-Meyer lemmas and elements of chomology. |
Content |
1. Elements of Fredholm operator theory
2. Infinite dimensional manifolds 3. Fiber bundles 4. Imersions, submersions 5. Transversality 6. Theorems of Ereshmann type 7. Finsler manifolds 8. Elements of homology and cohomology theory. Singular homology and Alexander-Spanier cohomology. 9. Morse and Gromoll-Meyer lemmas 10.Applications in geodesics. |
References |
1. Serge Lang, Introduction to Differentiable Manifold, Interscience, New-York, 1962.
2. R. Abraham, J. Robbin, Transversal mapping and flows, W.A. Benjamin, Inc. New York, Amsterdam, 1967. 3. K. C. Chang, Infinite dimensional Morse theory, Birkhauser, Boston, Basel, Berlin, 1993. 4. R. S. Palais, Morse theory on Holbrt manifolds, Topology 2(1963), 299-340. 5. R.S. Palais, Lusternuk-Schnirelmann theory on Banach manifolds, Topology 5 (1966), 115-132. 6. J. Margalef -Roig, E.O. Dominguez, Differential Topology, North-Holland,1992. 7. E.H. Spanier, Algebraic topology, Mc.Graw-Hill,1966. |
Assessment |
Exam. |