Algebraic Topology II

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English

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Algebraic Topology II

Semester
SoSe 2021

Lecturer
Pavel Sechin

Type of course (Veranstaltungsart)
Vorlesung

Contents
This is a continuation of the course "Algebraic Topology I" of WiSe 20/21. The following topics will be covered (* if time permits):

higher homotopy groups, fibrations and cofibrations;
Hurewicz theorem, Whitehead theorem, Freudenthal theorem, *Blackers-Massey theorem;
vector bundles, *principal G-bundles and their classifying spaces, characteristic classes;
the Serre spectral sequence.

This course is complemented by the seminar "Topological K-theory" (organized by M. Hoyois).

Literature

T. tom Dieck, Algebraic Topology, Vol. 8. European Mathematical Society, 2008.

A. Hatcher, Algebraic Topology, 2001.

A. Hatcher, Vector bundles and K-theory, 2003.

J. Milnor and J.D. Stasheff, Characteristic Classes, Annals of mathematics studies 76 (1975).

Recommended previous knowledge
Algebraic Topology I, basics of category theory (Yoneda lemma, limits and colimits, equivalences of categories, adjoint functors)

Time/Date
Tuesday 12-14, Thursday 12-14

Location
digital

Registration

Registration for the exercise classes: via GRIPS
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Successful participation in the exercise classes: 50% of points in the exercises, presentation
of a solution in class

Examination (Prüfungsleistungen)

Oral exam: Duration: 30 minutes, Date: first week after the lecture period, re-exam: Date: by
individual appointment

Modules
BV, MV, MArGeo, MGAGeo

ECTS
9