Subject: Critical Points and Applications	Code: MG264	

Semester	 Hours: C+S+L	Type	 Section	
1	2+1+1	compulsory	Algebra and Geometry - in English	

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 ""-category of a Pair of Manifolds;
   3.2 Some Homotopical Aspects;
   3.3 Some Pairs of Manifolds with infinite ""-category;
   3.4 Imersions with Infinitely many Zeros of Gauss-Kronecker curvature.	
Selective References	1. BURGHELEA, D., HANGAN, TH. MOSCOVICI, 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	Reports+Exam