- Docente: Sergio Venturini
- Credits: 6
- SSD: MAT/03
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Sep 19, 2024 to Dec 20, 2024
Learning outcomes
At the end of the course, the student acquires advanced knowledge on smooth manifolds and differential calculus with particular regard to de Rham cohomology and Morse theory. It is able to apply the acquired notions for solving problems and building demonstrations.
Course contents
Differentiable manifolds.
Submanifolds.
Differentiable functions.
Introduction to transversality.
Morse and Sard theorems.
Tangent space to a manifold.
Vector fields.
Distributions and Frobenius theorem.
Vector bundles.
Differential forms.
Exterior derivative.
Introduction to Riemannian geometry.
orientation and Stokes theorems.
De Rham cohomology.
Readings/Bibliography
L. Tu, Introduction to manifolds.
F. Warner, Foundations of differentiable manifolds and Lie groups.
J. M. Lee, Introduction to smooth Manifolds, (GTM Springer).
Teaching methods
Frontal Lessons
Assessment methods
The exam related to this component of the integrated course (00474 - DIFFERENTIAL GEOMETRY - 6 credits) consists of an oral test.
The exam mark attributed to the student is given by the average of the marks awarded for the two modules of the course, with rounding to the upper unit. The mark 29 does not preclude 30L as final mark.
Office hours
See the website of Sergio Venturini