Algebraic KTheory and the Wall finiteness obstructionSummer term 2021 
Lecturer: Christoph Winges Email: christoph dot winges at ur dot de Lectures: Friday, 10:15 Location: Zoom Tutorial: Tuesday, 16:15 Location: Zoom Further links: GRIPS (UR account required) KVV 
NewsIf you are planning to take the exam at the end of the term, please get in touch with me so we can arrange a date.The Zoom coordinates for lectures and tutorials will be announced on GRIPS. If you do not have a UR account but would like to attend the lectures, please contact me via email. 

OverviewThis course covers some applications of algebraic Ktheory (in particular the class group K_0) in geometric/algebraic topology. We will primarily cover the Wall finiteness obstruction which is a Ktheoretic invariant designed to detect whether certain topological spaces are homotopy equivalent to finite CWcomplexes. After discussing the fundamentals of the finiteness obstruction, we will develop some Ktheoretic machinery to give a proof of West's theorem. As an application of West's theorem, we will see that every compact topological manifold has the homotopy type of a finite CWcomplex.Prerequisites: basic algebraic topology (it should be possible to attend this lecture concurrently with Algebraic Topology II), some category theory; some acquaintance with simplicial homotopy theory will be helpful for the later parts of the lecture, but the necessary material can also be covered in the lecture as we get to that point 

Lecture NotesI will try to maintain TeXed lecture notes. The latest version is available here (last update 20210714 23:00).If you find typos or mathematical mistakes, I will be happy to learn about them.  
Exercise sheetsSolutions to the exercises requiring written solutions can be submitted via GRIPS or email.Sheet 1, for discussion during the first tutorial Sheet 2, due on 30th April, 16:00 Sheet 3, due on 7th May, 16:00 Sheet 4, due on 14th May, 16:00 Sheet 5, due on 28th May, 16:00 Sheet 6, due on 4th June, 16:00. 20210604: made a correction to the flavour text after the actual exercises, Sheet 6 with solutions, hopefully without too many typos and sign mistakes Sheet 7, due on 11th June, 16:00, Sheet 7 with solutions Sheet 8, due on 18th June, 16:00 Sheet 9, due on 25th June, 16:00 Sheet 10, due on 2nd July, 16:00 Sheet 11, due on 9th July, 16:00 

ExamThe final examination will take the form of an oral exam. Scoring at least 50 percent of all possible points on the exercise sheets will be sufficient to qualify for the final exam. 

Literature

Last modified 20210701, 19:00