Abstract
A variety of computations regarding the Euler class group E ( A n , A n ) and the Grothendieck group K 0 ( A n ) of the algebraic sphere Spec ( A n ) is done. The Euler class of the algebraic tangent bundle on Spec ( A n ) is computed. It is also investigated whether every element in the Euler class group E ( A n , A n ) is the Euler class of a projective A n module of rank n.
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