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

Algebraic and differential topology (1)
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MG251
1
2+2+0
9
compulsory
Algebră şi Geometrie
Teaching Staff in Charge
Prof. ANDRICA Dorin, Ph.D., dandrica@math.ubbcluj.ro
Aims
The main purpose of this course consists in presentation of the basic problems of Differential Topology. Some important results concerning the smooth manifolds and smooth mapping as well some applications are given. Some results obtained by Chair of Geometry in the study of critical points of mappings beetwen differentiable manifolds are included in chapter 3.
Content
1. The global theory of smooth mappings between manifolds. Global constructions of
smooth mappings (smooth partition of unity). Differentiable submanifolds. Manifolds
with boundary. Homotopy and isotopy of smooth mappings. The modulo 2 degree and some applications.
2. Fundamental results in Differential topolgy. Sets of zero measure on a manifold.
Sard'theorem and applications. Whitney'embeding theorem.
3. The study of critical points of mappings between manifolds. The critical set and the bifurcation set. Sufficient conditions for the infiniteness of the critical set. The
G-equivariant and G-invariant cases.Some geometric applications.
References
1. Andrica,D.,Critical Point Theory and Some Applications, University of Ankara,1993
2. Andrica,D.,Pintea,C.,Spatii de acoperire cu aplicatii in teoria punctului critic, Universitatea "Babes-Bolyai" Cluj-Napoca, va apare
3. Andrica,D.,Pintea,C.,Functii cu numar minim de puncte critice, Presa Universitara Clujeana, in pregatire
4. Conlon,L.,Differentiable Manifolds.A First Course, Birkhauser,1993
5. Jost,J.,Riemannian Geometry and Geometric Analysis, Springer Verlag,1995
Assessment
Oral examination