Enrollment year
2018/2019
Academic discipline
MAT/03 (GEOMETRY)
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Curriculum
PERCORSO COMUNE
Period
1st semester (01/10/2020 - 20/01/2021)
Lesson hours
56 lesson hours
Activity type
WRITTEN AND ORAL TEST
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.
Sustainable development goals - Agenda 2030
Università di Pavia - Offerta formativa