论文标题
射影齿状歧管上的矢量场和布劳德 - 杜邦不变
Vector fields on projective Stiefel manifolds and the Browder-Dupont invariant
论文作者
论文摘要
我们在投影stiefel歧管的跨度$ x_ {n，r} = o（n）/（o（n-r）\ times \ times \ mathbb z/2）$中开发了强下界，这使得非常准确（在许多情况下是精确的）跨度的估计值。该技术在大多数情况下涉及向量束的基本稳定性。但是，带有$ n $奇数的情况$ x_ {n，2} $带来了额外的困难，这些困难是通过Browder-dupont不变的部分解决的。在此过程中，我们观察到，由于所有奇数封闭的歧管，由于Sutherland引起的对称升力并不一定存在，因此，正如他所制定的那样，Browder-dupont不变型通常并未定义。我们将表征$ x_ {n，2} $上明确定义的browder-dupont不变性的那些$ n $。然后在这种情况下将使用不变性，以获得跨度的下限，作为更强结果的推论。
We develop strong lower bounds for the span of the projective Stiefel manifolds $X_{n,r}=O(n)/(O(n-r)\times \mathbb Z/2)$, which enable very accurate (in many cases exact) estimates of the span. The technique, for the most part, involves elementary stability properties of vector bundles. However, the case $X_{n,2}$ with $n$ odd presents extra difficulties, which are partially resolved using the Browder-Dupont invariant. In the process, we observe that the symmetric lift due to Sutherland does not necessarily exist for all odd dimensional closed manifolds, and therefore the Browder-Dupont invariant, as he formulated it, is not defined in general. We will characterize those $n$'s for which the Browder-Dupont invariant is well-defined on $X_{n,2}$. Then the invariant will be used in this case to obtain the lower bounds for the span as a corollary of a stronger result.
