Università di Pavia - Offerta formativa
Language: it en
TOPICS IN GEOMETRY
Stampa
Enrollment year
2017/2018
Academic year
2019/2020
Regulations
DM270
Academic discipline
MAT/03 (GEOMETRY)
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Course
MATHEMATICS
Curriculum
PERCORSO COMUNE
Year of study
3°
Period
1st semester (30/09/2019 - 10/01/2020)
ECTS
6
Lesson hours
56 lesson hours
Language
Italian
Activity type
WRITTEN AND ORAL TEST
Teacher
PERNAZZA LUDOVICO (titolare) - 6 ECTS
Prerequisites
The basic notions of group theory, linear algebra and general topology.
Learning outcomes
An introduction to homotopy and homology
Course contents
The fundamental group. Free groups. The theorems of Van Kampen.
Covering spaces.
Basic notions of homological algebra. Singular homology and its homotopic properties, relative homology, axiomatic homology theory. Simplicial complexes, CW-complexes. Triangulations, Euler-Poincarè characteristic, orientation, the classification of surfaces. Jordan curve theorem, invariance of domain.
Teaching methods
Lectures and problem sessions
Reccomended or required readings
A. Hatcher: "Algebraic Topology", Cambridge University Press (freely available online)
M. Greenberg, J. Harper: "Algebraic Topology".
W. Massey: "A Basic Course in Algebraic Topology", Springer-Verlag.
E. Spanier: "Algebraic Topology".
Assessment methods
Written and oral exam.
Further information
Sustainable development goals - Agenda 2030

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