Universität Regensburg   IMPRESSUM    DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
Algebraic Topology
Semester
WiSe 2018 / 19

Lecturer
Clara Löh

Type of course (Veranstaltungsart)
Vorlesung

Contents
Algebraic topology studies topological spaces via algebraic invariants -- by modelling certain aspects of topological spaces in the realm of algebra, e.g., by groups and group homomorphisms. Classical examples include homotopy groups and (co)homology theories.

Algebraic topology has various applications, both in theoretical and in applied mathematics, for instance, through fixed point theorems and (non-)embeddability results. For example, Nash's proof of existence of certain equilibria in game theory is based on a topological argument.

Moebius

Topics covered in this course include:
  • What is algebraic topology?
  • The fundamental group and covering theory
  • the Eilenberg-Steenrod axioms
  • singular (co)homology
  • cellular (co)homology
  • classical applications of (co)homology.
This course will be complemented with the course "Group Cohomology" in the summer 2019, where (co)homology of groups will be studied. The course in SS 2019 can also be attended independently of the present course on Algebraic Topology.

Literature
will be announced at the beginning of the course

Recommended previous knowledge
Analysis I,II,(IV), Algebra (groups, rings, modules; basic homological algebra is helpful, but not strictly required)

Time/Date
Mo 10-12, Thu 10-12

Location
Mo: M102, Thu: M104

Course homepage
http://www.mathematik.uni-r.de/loeh/teaching/topologie1_ws1819
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

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: via GRIPS in the first week of lecture period
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Successful participation in the exercise classes: 50% of the credits, presentation of
    a solution in class
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 25 minutes, Date: individual, re-exam: Date: individual
Regelungen bei Studienbeginn vor WS 2015 / 16
  • Benotet:
    • O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung
  • Unbenotet:
    • O. g. Studienleistung
Modules
BV, MV, MGAGeo

ECTS
9
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