Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT

Code	Subject	
MG264	Critical Points and Applications	

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

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 CRITICAL POINTS OF MAPPINGS BETWEEN MANIFOLDS
   3.1 Functions with finitely many critical points
   3.2 Functions with infinitely many critical points.	
Bibliography	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., Continuous Mappings with an Infinite Number of Topologically Critical Points, Annales Polonici Mathematici, LXVII.1, 1997.
5. PINTEA, C., Geometrie. Geometrie Diferentiala, Geometrie Riemannian. Grupuri si Algebre Lie, Presa Universitara Clujeana, 2006.

Assessment	Exam+Quiz+Reports.