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Geometry 5

A.Y. 2018/2019
9
Max ECTS
77
Overall hours
SSD
MAT/03
Language
Italian
Learning objectives
The aim of the course is to give elements of Covering Theory and of De Rham cohomology
Expected learning outcomes
To be able to recognize a covering space and its basic properties. To be able to classify the coverings of a given topological space via its fundamental group.
To be able to compute de Rham cohomology of simple differentiable manifolds.

Lesson period: First semester

Lessons timetable

Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi

Exams calendar

Single course

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Course syllabus and organization

Single session

Responsible
Stellari Paolo
Lesson period
First semester
Website
Geometry 5 (first part)
Course syllabus
Fundamental group and Seifert Van Kampen theoren. CW complexes.
Topological coverings and their properties.
Monodromy. Universal covering. ClassificationTheorem.
Homological Algebra.
de Rham complex and cohomology. Mayer-Vietoris sequence. Poincaré lemma. Finiteness theorems.
Geometry 5 mod/2
Course syllabus
All the topics of the 6 cfu version and:
Poincaré lemma. Cohomology with compact supports, Poincaré duality.
Hints on homology and on de Rham Theorem.
Geometry 5 (first part)
MAT/03 - GEOMETRY - University credits: 6
Practicals: 11 hours
Guided problem-solving: 6 hours
Lessons: 36 hours
Professors: Colombo Elisabetta, Stellari Paolo
Geometry 5 mod/2
MAT/03 - GEOMETRY - University credits: 3
Guided problem-solving: 6 hours
Lessons: 18 hours
Professors: Colombo Elisabetta, Stellari Paolo
Professor(s)
Colombo Elisabetta
Reception:
friday.8.45-11.45
Office2101, second floor, via C. Saldini 50
Stellari Paolo
Web site
Reception:
Fix an appointment by email
Dipartimento di Matematica "F. Enriques" - Room 2046