Stable Real Cohomology of SL_n(Z)

Specialeforsvar ved Mikala Ørsnes Jansen

Title: Stable Real Cohomology of SL_n(Z)

Abstract: The aim of this thesis is to calculate the real cohomology of the special linear group SL_n(Z) in low degrees. This is a special case of Borel's article Stable Real Cohomology of Arithmetic Groups from 1974 and Borel and Serre's article Corners and Arithmetic Groups from 1973. In fact, the ambition of this project is to provide a stepping stone towards understanding these articles by looking at the details of the special case while avoiding use of the general theory. To calculate the real cohomology of SL_n(Z), we exploit the geometric setting: We cover Siegel reduction theory, the Borel-Serre compactification, logarithmic differential forms and Matsushima's Vanishing Theorem 

Vejleder:  Dustin Clausen
Censor:    Martin Raussen, Aalborg Universitet