For n = 2m+1 - 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) x SO(3). As an application, we provide not only a lower but also an upper bound for the LS-category of G̃ n,3. We also study the immersion problem of G̃n,3.
|Number of pages||15|
|Journal||Homology, Homotopy and Applications|
|Publication status||Published - 2008|
- Gröbner bases
ASJC Scopus subject areas
- Mathematics (miscellaneous)