论文标题
Stiefel-Whitney类以及可定向和自旋歧管的沉浸
Stiefel-Whitney classes and immersions of orientable and Spin manifolds
论文作者
论文摘要
我们为最大的欧几里得空间确定了一个不错的简单公式，在该空间中有一个可定向的N-manifold，并由Stiefel-Whitney类检测到非剥离。对于自旋歧管，我们证明了上限的类似物，并为n <24和n = 33,34建立了完整的答案。与其中许多相似的结果是在大约50年前获得的，但以较低的方式进行。自旋歧管的尖锐结果需要对Mod-2 eilenberg-Maclane空间的KO-andology组进行详细计算。
We determine a nice simple formula for the largest Euclidean space for which there is an orientable n-manifold with a nonimmersion detected by Stiefel-Whitney classes. For Spin manifolds, we prove the analogue of the upper bound and establish the complete answer for n<24 and n=33,34. Results similar to many of these were obtained some 50 years ago, but in a much less tractable form. The sharp results for Spin manifolds require detailed calculations of ko-homology groups of mod-2 Eilenberg-MacLane spaces.
