Gröbner Bases of Oriented Grassmann Manifolds
نویسنده
چکیده
For n = 2 − 4, m > 2, we determine the cup-length of H∗(G̃n,3;Z/2) by finding a Gröbner basis associated with a certain subring, where G̃n,3 is the oriented Grassmann manifold SO(n + 3)/SO(n)× SO(3). As an application, we provide not only a lower but also an upper bound for the LS-category of G̃n,3. We also study the immersion problem of G̃n,3.
منابع مشابه
Application of Gröbner Bases to the Cup-length of Oriented Grassmann Manifolds
Let R be a commutative ring. The cup-length of R is defined by the greatest number n such that there exist x1, . . . , xn ∈ R \ R with x1 · · · xn , 0. We denote the cup-length of R by cup(R). In particular, for a space X and a commutative ring A, the cup-length of X with the coefficient A, is defined by cup(H̃(X; A)). We denote it by cupA(X). It is well-known that cupA(X) is a lower bound for t...
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تاریخ انتشار 2008