Groebner Bases and the Cohomology of Grassmann Manifolds with Application to Immersion
نویسنده
چکیده
LetGk,n be the Grassmannmanifold of k-planes inR . Borel showed that H∗ (Gk,n; Z2) = Z2 [w1, . . . , wk] /Ik,n where Ik,n is the ideal generated by the dual Stiefel-Whitney classes wn+1, . . . , wn+k. We compute Groebner bases for the ideals I2,2i−3 and I2,2i−4 and use these results along with the theory of modi ed Postnikov towers to prove new immersion results, namely that G2,2i−3 immerses in R i+2−15. As a bene t of the Groebner basis theory we also obtain a simple description of H∗ ( G2,2i−3; Z2 ) and H∗ ( G2,2i−4; Z2 ) and use these results to give a simple proof of some non-immersion results of Oproui.
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تاریخ انتشار 1997