"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Morse theory
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MG255
2
2+2+0
9
compulsory
Algebră şi Geometrie
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.