Topologia differenziale

A.Y. 2017/2018
6
Max ECTS
42
Overall hours
SSD
MAT/03
Language
Italian
Learning objectives
The aim of the course is to illustrate the main results and to provide some of the techniques of differential topology.
Expected learning outcomes
Know how to use some of the differential topology techniques on differentiable manifolds.
Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Course syllabus
Short review on: differentiable manifolds and maps; immersions and submersions; vector bundles.
Critical / regular points and critical / regular values. Sard's theorem. Whitney theorems. Transversality. Intersection theory. Winding numbers. Vector fields, the Hopf-Poincaré theorem.
General position; homotopy and stability.
Operations with vector bundles; cohomology of bundles. Ponicarè duality and Thom class.
Morse Functions. Passing critical leves and attaching cells. Cellular homology. Morse's inequality and equality.
MAT/03 - GEOMETRY - University credits: 6
Lessons: 42 hours
Professor(s)
Reception:
by appointment (by e-mail)
Math. Dept. - via C. Saldini 50 - Milano