论文标题
自旋^H和旋转的进一步概括
Spin^h and further generalisations of spin
论文作者
论文摘要
哪个流形的是旋转或旋转^C的问题，具有简单而完整的答案。在本文中，我们解决了旋转^H歧管的相同问题，该问题的研究较少，但在近几十年来出现在几何和物理学中。我们确定旋转^H的第一个障碍是第五个积分hitnney类W_5。此外，我们表明维度7或更低的每个紧凑的定向歧管都是旋转^H，并且在所有更高维度中都有可定向的歧管。然后，我们将考虑一般自旋结构的无限序列。在这样做时，我们表明没有整数k，因此每个歧管都嵌入了用编成k的旋转歧管中。
The question of which manifolds are spin or spin^c has a simple and complete answer. In this paper we address the same question for spin^h manifolds, which are less studied but have appeared in geometry and physics in recent decades. We determine that the first obstruction to being spin^h is the fifth integral Stiefel-Whitney class W_5. Moreover, we show that every compact orientable manifold of dimension 7 or lower is spin^h, and that there are orientable manifolds which are not spin^h in all higher dimensions. We are then led to consider an infinite sequence of generalised spin structures. In doing so, we show that there is no integer k such that every manifold embeds in a spin manifold with codimension k.
