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Algebraic Topology I SemesterWiSe 2023 / 24 Lecturer Marc Hoyois Type of course (Veranstaltungsart) Vorlesung German title Algebraische Topologie I Contents Algebraic topology studies topological spaces by means of algebraic invariants (groups, vector spaces, etc.), which allow us to reduce questions in topology to questions in algebra. Algebraic topology has many applications, both in theoretical and in applied mathematics. Nowadays, a basic knowledge of algebraic topology is essential in most other fields of pure mathematics, including analysis, algebraic geometry, and number theory. In applied mathematics, topological data analysis is a relatively new field that relies heavily on tools from algebraic topology. In this first course on algebraic topology, we will study in depth two important invariants of a topological space: its fundamental group and its (co)homology groups. We will also see how to use these algebraic invariants to answer some interesting topological questions. Topics covered in this course include:
Recommended previous knowledge Algebra (groups, rings, modules), topological spaces Time/Date Di 8-10, Do 10-12 Location M101 Course homepage https://elearning.uni-regensburg.de/course/view.php?id=62374 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
There will be a weekly exercise session, Do 12-14 M102 Modules BV, MV, MArGeo, MGAGeo ECTS 9 |