SUPPLEMENT TO TOPOLOGY
Learning outcomes of the course unit
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.
Knowledge of basic topics of general topology (compactness, connectedness, continuity...) and algebra (groups, normal subgroups, quotient groups) are prerequisites.
Course contents summary
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.
C. Kosnioski, Introduzione alla topologia algebrica, Zanichelli