TITLE: Groebner Bases and the Cohomology of Grassmann Manifolds with
       Application to Immersion

AUTHOR: Ken Monks
        Department of Mathematics
        University of Scranton
        Scranton, PA 18510
        email: monks@uofs.edu

FILENAME: GRASS.DVI

ABSTRACT:

Let G_{k,n} be the Grassmann manifold of k-planes in R^{n+k}. Borel showed
that H^*( G_{k,n}; Z_2) = Z_2[w_1,...,w_k] /I_{k,n} where I_{k,n} is the
ideal generated by the dual Stiefel-Whitney classes
\overline{w}_{n+1},...,\overline{w}_{n+k}. We compute Groebner bases for the
ideals I_{2,2^i-3} and I_{2,2^i-4} and use these results along with the
theory of modified Postnikov towers to prove immersion results, namely
that G_{2,2^i-3} immerses in R^{2^{i+2}-15}.  As a benefit of the Groebner
basis theory we also obtain a simple description of H^*(G_{2,2^i-3};Z_2) and
H^*(G_{2,2^i-4};Z_2)  and use these results to give a simple proof of some
non-immersion results of Oproui.