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Abstract  

We present some non-vanishing dual Stiefel-Whitney classes of the Grassmann manifolds O(n)/O(4) × O(n − 4) for n = 2s + 2 and n = 2s + 3 (s ≧ 3), providing a supplement to results of Hiller, Stong, and Oproiu. Some applications are also mentioned.

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Summary  

It is well known that Dold and Milnor manifolds give generators for the unoriented bordism algebra N * over  Z 2. The purpose of this paper is to determine those Milnor manifolds which represent the same bordism classes in N *  as their Dold counterparts.

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Abstract  

We prove new results about the vector field problem on the real flag manifolds O(n)/O(1) x O(1) x O(n - 2). For some infinite families of these manifolds, we completely solve the vector field problem.

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