Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea magistrale in Mathematics - Enrollment from 2025/2026The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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2° Year activated in the A.Y. 2011/2012
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Due tra i seguenti insegnamenti
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Due tra i seguenti insegnamenti
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Legend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Differential geometry and topology (2010/2011)
Teaching code
4S02812
Credits
12
Language
Italian
Scientific Disciplinary Sector (SSD)
MAT/03 - GEOMETRY
The teaching is organized as follows:
Teoria
Esercitazioni
Learning outcomes
Learning objectives
The course delves further into general topology and introduces the basic notions of algebraic
and differential topology, focussing on the concept of differentiable manifold. Furthermore, the
elements of Riemannian geometry will be introduced as well.
The course, suitable to both curricula (didactic and applied) will be quite concrete and based
on examples also coming from other areas of mathematics.
Program
Course Programme
General topology (continued). Separation. Quotients.
Fundamental group. Covering spaces.
Differentiable manifolds.
De Rham's theory.
Riemannian manifolds.
Levi-Civita connection.
Curvature tensors (Riemann, sectional, Ricci, scalar).
Geodesics and their variational aspects.
Exponential map.
Lie groups. Symmetric spaces.
Riemann surfaces and algebraic curves.
Vector bundles, Euler's class and number, Euler-Poincare' characteristic.
The Poincare'-Hopf theorem.
Examination Methods
Written test, followed by an oral exam.
Teaching materials e documents
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note sansonetto (it, 354 KB, 2/4/11)
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programma ufficiale topogeo 2010/11 (it, 45 KB, 1/17/11)
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topogeo-16-2-11 (it, 206 KB, 2/16/11)
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topogeoI (it, 432 KB, 9/12/10)
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topogeo-scritto 1-7-11 (it, 200 KB, 7/7/11)
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topogeo-scritto 19-9-11 (it, 209 KB, 9/19/11)
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topogeoXLI (it, 355 KB, 1/12/11)
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topogeoXLII (it, 445 KB, 1/19/11)
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topogeoXLIII (it, 371 KB, 1/19/11)
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topogeoXLIV (it, 304 KB, 1/19/11)
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topogeoXXIX-add (it, 30 KB, 11/24/10)
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topogeoXXVI-add (it, 91 KB, 11/22/10)
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topogeoXXXII-add (it, 196 KB, 11/30/10)