Universitatea "Babeş-Bolyai" din Cluj-Napoca

Facultatea de Matematică şi Informatică
FISA DISCIPLINEI

Teoria Morse Morse theory
Cod
Semes-
trul
Ore: C+S+L
Credite
Tipul
Sectia
MG255
2
2+2+1
10
obligatorie
Algebra şi Geometrie
(Algebra and Geometry)
Cadre didactice indrumatoare Teaching Staff in Charge
Conf. Dr. VARGA Csaba Gyorgy, csvarga@cs.ubbcluj.ro
Obiective Aims
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.
Continut
1. Elemente de teoria operatorilor Fredholmi.
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.
Bibliografie
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
Examen
Exam.