19217011 Seminar zur Topologie
Sommersemester 2018
Dozenten: Prof. Dr. Holger Reich, Prof. Dr. Elmar Vogt
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Zeit und Ort: Montag 12:00-14:00 Uhr, Arnimallee 6, SR 025/026
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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.
Vorträge/Talks
| Termin | Titel | Vortragende(r) |
|---|---|---|
| 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 |
Participation
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.
Literature
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.