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

Critical points and applications
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MG264
1
2+1+1
8
compulsory
Algebră şi Geometrie - în limba engleză
Teaching Staff in Charge
Assoc.Prof. PINTEA Cornel, Ph.D., cpintea@math.ubbcluj.ro
Aims
The course is studing on the one hand the local behaviour of a real differentiable function around a non-degenerate critical point and the Morse Theory as an immediate application, and on the other hand is studing the critical set of mappings with values in manifolds of dimension greater than one.
Content
I. ELEMENTS OF CRITICAL POINT THEORY
1.1 Generalties on Critical Point Theory;
1.2 The first Deformation Lemma;
1.3 The second deformation Lemma;
II. MORSE THEORY AND APPLICATIONS
2.1 Morse Lemma;
2.2 Passing a critical level;
2.3 Morse Inequalities;
III. SOME ASPECTS OF CRITICAL POINT THEORY OF MAPPINGS WITH VALUES IN SPACES OF DIMENSION GREATER THAN ONE
3.1 The $\varphi$-category of a Pair of Manifolds;
3.2 Some Homotopical Aspects;
3.3 Some Pairs of Manifolds with infinite $\varphi$-category;
3.4 Imersions with Infinitely many Zeros of Gauss-Kronecker curvature.
References
1. Burghelea, D., Hangan, Th. Moscivici, H., Verona, A., Introducere in topologia diferentiala, Ed. Stiintifica, Bucuresti, 1973.
2. Milnor, J., Morse Theory, Annals of Math. Studies, Princeton Univ. Press, 1963.
3. Palais, R.S., Terng, C-L., Critical Point Theory and Submanifold Geometry, Lectures Notes in Mathematics, Springer-Verlag.
4. Pintea., C., Teza de Doctorat, Universitatea de Vest din Timisoara, 1996.
5. Pintea, C., Continuous Mappings with an Infinite Number of Topologically
Critical Points, Annales Polonici Mathematici, LXVII.1, 1997.
6. Pintea, C., Differentiable Mappings with an Infinite Number of Critical Points,
Proceedings of the American Mathematical Society, Vol. 128, Nr. 11, 2000.
7. Raileanu, L., Varietati topologice si diferentiale, Lit. Univ. $Al. I. Cuza$ Iasi, 1984.
Assessment
Exam.