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Title  Groebner Bases And The Cohomology Of Grassmann Manifolds With Application To Immersion  Author(s)  Kenneth G. Monks  Type  Technical Report, Misc  Abstract  Let G k,n be the Grassmann manifold of kplanes in R^(n+k). Borel showed that H*(G k,n ; Z2) = Z2 [w1, ... ,wk]/I k,n where I k,n is the ideal generated by the dual StiefelWhitney classes wn+1, ... ,wn+k. We compute Groebner bases for the ideals I 2,2 Gamma4 and use these results along with the theory of modified Postnikov towers to prove new immersion results, namely that G 2,2 Gamma3 immerses in R^(2?+3)15. As a benefit of the Groebner basis theory we also obtain a simple description of H (G2,2?3;Z2) and H*(G2,2?4;Z2) and use these results to give a simple proof of some nonimmersion results of Oproui. 
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 Language  English  Year  1997  Edition  0  Translation 
No  Refereed 
No 
