IMPRESSUM    DATENSCHUTZ
	Fakultät für Mathematik	Universität Regensburg
Algebraic Topology I Semester WiSe 2024 / 25 Lecturer Denis-Charles Cisinski Type of course (Veranstaltungsart) Vorlesung German title Algebraische Topologie I Contents Algebraic Topology is the systematic study of topological spaces through algebraic invariants. We will study the simplest one first: the set of connected components. We will go further in our study of connectivity through the theory of coverings and their classification by Poincaré's fundamental group. In order to reach higher dimensional algebraic invariants, we will go in the direction of singular homology. We will see applications such as several proofs of the fundamental theorem of Algebra, or Brouwer's fixed point theorem Literature Bourbaki, Topologie Algébrique, Springer Laures and Szymik, Grundkurs Topologie, Springer Switzer, algebraic Topology, Springer Recommended previous knowledge basics of topological spaces Time/Date Tuesday and Thursday, 14-16h Location M103 Registration Preliminary registration for the organisation of exercise classes: at the end of the previous semester via EXA or LSF (see announcement by the department) Registration for the exercise classes: on GRIPS Registration for course work/examination/ECTS: FlexNow Course work (Studienleistungen) Successful participation in the exercise classes: you should get about 40% of the points in the exercises Examination (Prüfungsleistungen) Oral exam: Duration: 30 min, Date: by appointment, re-exam: Date: Modules BV, MV, MGAGeo ECTS 9

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