| Teoria Morse | Morse theory |
trul |
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(Algebra and Geometry) |
| Cadre didactice indrumatoare | Teaching Staff in Charge |
| Conf. Dr. VARGA Csaba Gyorgy, csvarga@cs.ubbcluj.ro |
| Obiective | Aims |
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Cursul are ca scop constructia principalelor instrumente pentru studiul varietatilor diferentiabile infinite dimensionale. In cadrul cursului se predau notuni de teoria operatorilior Fredholmi, varietati Banach infinit dimensionale, imersii si submersii, transversalitate, teoreme de tip Ereshmann, lema lui Morse si elemente de teoria omologiei si coomologie. |
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. |
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1. Elemente de teoria operatorilor Fredholm.
2. Varietati Banach infinit dimensionale. 3. Fibrate Banach vectoriale. 4. Imersii si submersii. 5. Transversalitate. Teorema de transversalitate a lui Abraham. 6. Teoreme de tip Ereshmann. 7. Varietati Finsler. 8. Elemente de teoria omologiei si coomologiei. Omologia si coomologia singulara si Alexander-Spanier. 9. Lema lui Morse si a lui Gromoll-Meyer. 10. Aplicatii in teoria geodezicelor. |
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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. |
| Evaluare | Assessment |
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Examen |
Exam. |