ELEMENTS OF ADVANCED GEOMETRYModule SECOND PART
Academic Year 2023/2024 - Teacher: Angelo BELLAExpected Learning Outcomes
Fundamental aspects of Algebraic Topology. Principal objects of the study are the fundamental group and some relevant facts of omotopy theory.
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. Dugundji "Topology"