TOPOLOGIA ALGEBRICA
Academic Year 2021/2022 - 1° Year - Curriculum APPLICATIVOCredit Value: 6
Scientific field: MAT/03 - Geometry
Taught classes: 35 hours
Exercise: 12 hours
Term / Semester: 2°
Learning Objectives
Fundamental aspects of Algebraic Topology. Principal objects of the study are the omotopy theory and the singular homology groups.
Course Structure
Lectures with slides. Discussion and correction of exercises.
If the teaching is given in a mixed or remote mode, the necessary changes may be introduced with respect to what was previously stated, in order to respect the program envisaged and reported in the syllabus.
Detailed Course Content
Basic facts on algebraic topology. Homotopy theory. Degree of a function between n-spheres. Brower's theorem in general form. Singular homology groups. The exact sequence of a pair. Mayer-Vetoris's sequence. Another proof of Brower's theorem. Jordan's theory in general form.
Textbook Information
1. Professor's notes
2. "Topologia" by M. Manetti.
3. W. Massey"Singular homology theory