Details:

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 k-planes 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 Stiefel-Whitney 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 non-immersion results of Oproui.
File
Language	English
Year	1997
Edition	0
Translation	No
Refereed	No