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Forschungsmodul: Topologie "Algebraic K-Theory"

Winter Term 2017/2018

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

  • Time and Place:  Tuesday, 14:00-16:00 h, Arnimallee 7, SR 031


In this seminar we want to study algebraic K-theory. To every ring R (or more generally to every exact category, or Waldhausen category, or stable infinity-category) one associates a space (or spectrum), whose homotopy groups are denoted K_i(R). While K_0(R) and K_1(R) have very simple and concrete algebraic descriptions, higher algebraic K-theory groups are more involved and usually very difficult to compute.
Whereas the first talks in the seminar may only need basic knowledge in algebra, we will later also use concepts from algebraic topology and in particular homotopy theory. 

The seminar language is English.


17.10.       Preliminary Discussion
Holger Reich / 
Elmar Vogt
24.10.      Discussion  
07.11.  1. Wall’s finiteness obstruction Tatiana Levinson 
14.11.  2. K_0 of Dedekind domains Alberto Richtsfeld 
21.11.  3. K_2 and universal central extensions Alexander Müller 
28.11.  4. The K-theory space I Georg Lehner 
05.12.  5. The K-theory space II Robert Cardona 
12.12.  6. The additivity theorem I Vincent Boelens 
19.12.  7. The additivity theorem II Vincent Boelens 
09.01.  8. Quillen’s Q-construction Anna Buhné 
16.01.  9. Quillen’s plus construction  
23.01.  10. Negative K-theory  
30.01.  11. Assembly maps  
06.02.  TBA  
13.02.  TBA  


J. Milnor: Introduction to Algebraic K-Theory, Ann. of Mathematics Studies Number 72, 1971
I. Madsen and I. Patchkoria: Notes for Categories and Toplogy, Univ. Copenhagen, 2016