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19217011 Seminar zur Topologie

Sommersemester 2018

Dozenten:  Prof. Dr. Holger Reich, Prof. Dr. Elmar Vogt

  • Zeit und Ort:  Montag 12:00-14:00 Uhr, Arnimallee 6, SR 025/026

  • Leistungsnachweis:  Vortrag und schriftliche Vortragsausarbeitung.

Content:  Vector bundles and K-theory

Vector bundles and, related to them, K-Theory play an important role in many areas of mathematics. Roughly, a real (complex) vector bundle over a space X is a family of real (complex) vector spaces parametrized by the points x of X which vary continuously with x, and K-theory associates to a space X an abelian group which contains the isomorphism classes of vector bundles over X as an abelian semigroup in a natural way. Vector bundles and K-theory have the advantage that they are accessible without too many prerequisites: a good understanding of linear algebra and basic topology suffice to develop a rich theory which has been used to solve several deep problems in geometric topology and homotopy theory.

The seminar is intended for bachelor and master students with earlier talks suited for bachelor students. There is very little overlap with parts 2 and 3 of the usual topology lectures, rather the seminar broadens the view on what algebraic topology is about.


17.04. Vorbesprechung / preliminary discussion Holger Reich
23.04. Vector bundles I Elmar Vogt
30.04. Vector bundles II Elmar Vogt/
Daniel Reusche
07.05. Vector bundles III Daniel Reusche
14.05. Homotopy theoretic interpretation of vector bundles Marco Flores
28.05. Bott periodicity I Viktor Tabakov
04.06. Bott periodicity II Amelie Flatt
11.06. Bott periodicity III Daniel Krupa
18.06. Homotopy Theory Summer - Berlin 2018  
25.06. Homotopy Theory Summer - Berlin 2018  
02.07. The Hopf invariant Vincent Boelens


If you are interested in participating please send an email to both organizers and attend the first meeting on 17.04. If there are several interested students, who have a conflict with the time slot we may try to shift.


As a source for the talks we will use the book

  • Michael F. Atiyah: K-Theory, Benjamin 1967

with further literature for the individual talks.