Topology Seminar by Marco Schlichting

Abstract: For a commutative local ring R with infinite residue field, we show that 

H_i(SL_nR,SL_{n-1}R; \Z) = 0 for i<n and we give a presentation of that group for i=n.

This leads to the definition of an Euler class for oriented vector bundles over a noetherian scheme with infinite residue fields and the theorem that an oriented rank n vector bundle on an affine such scheme of dimension n has a global non-vanishing section if and only if its Euler class vanishes.