SUPPLEMENT TO TOPOLOGY
cod. 14857

Academic year 2007/08
3° year of course - Second semester
Professor
Academic discipline
Geometria (MAT/03)
Field
Formazione algebrico-geometrica
Type of training activity
Characterising
56 hours
of face-to-face activities
3 credits
hub:
course unit
in - - -

Learning objectives

The course aims to provide basic knowledge and technical skills in Algebraic Topology. The topics developed and the techniques acquired during the course are necessary, or in any case very important, for thorough learning of a wide spectrum of advanced mathematics topics, for example, differential geometry, real and complex analysis, differential topology and algebraic geometry.

Prerequisites

Knowledge of basic topics of general topology (compactness, connectedness, continuity...) and algebra (groups, normal subgroups, quotient groups) are prerequisites.

Course unit content

<br />Homotopy and relative homotopy between applications. Homotopic equivalence between spaces. Contractable spaces. Retracts and deformation retracts. Homotopy between paths. Fundamental group of a topological space. Fundamental group of the circumference. Covering maps and lifting property. Actions of groups and fundamental group of an orbit space. Free groups and their quotients. Van Kampen theorem. 

Full programme

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Bibliography

C. Kosnioski, Introduzione alla topologia algebrica, Zanichelli

Teaching methods

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Assessment methods and criteria

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Other information

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