Subject: Date: Wed, 22 Aug 2001 09:25:52 -0700 From: Vitali Kapovitch Question: I suspect that the following is well-known and if yes I would appreciate a reference. Let $X$ be a finite $CW$ complex. Then for any collection of cohomology classes $\chi\in H^{2k}(X),p_1\in H^4(X),...,p_{k-1}\in H^{4k-4}$ there exists an integer $m$ and a rank $2k$ vector bundle over $X$ whose Euler class is equal to $m\chi$ and whose Pontrjagin classes are given by $mp_1,..,mp_{k-1}$.