Module page
Geometry II
| academic year: | 2013/2014 |
| instructor: | Marco Manetti |
| degree course: | Mathematics - DM 270/04 (triennale), II year |
| type of training activity: | caratterizzante |
| credits: | 9 (72 class hours) |
| scientific sector: | MAT/03 Geometria |
| teaching language: | italiano |
| period: | II sem (03/03/2014 - 13/06/2014) |
Lecture meeting time and location
Presence: highly recommended
Module subject: Basic notions of general topology, compact and connected spaces. Quotient topology, locally compact spaces, numerability axioms, complete metric spaces, Baire theorem. Zorn's lemma, infinite products an Tychonoff theorem. HOmotopy and fundamental group, covering spsces and Van Kampen theorem. Paracompact spaces and topological manifolds. Differentiable manifolds, partitions of unity, vector fields, skethces on Lie groups and Lie algebras.
Suggested readings:
- Marco Manetti, Topologia.
- W. Boothby, An introduction to differentiable manifolds and Riemannian geometry (capitoli da 1 a 4) Teaching notes.
Type of course: standard
Useful link: http://www1.mat.uniroma1.it/people/manetti/didattica.html
Knowledge and understanding: Proficient students will be able to understand general topology, the basic concepts of homotopy theory and the notion of differentiable manifold.
Skills and attributes: Students will be able to understand teaching courses requiring the knowledge of general topology, basic homotopy theory and the notion of differential manifold.
Personal study: the percentage of personal study required by this course is the 65% of the total.