Faculty of Mathematics and Computer Science

Elements of algebraic and differential topology |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

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 |