Spin^h and further generalisations of spin

@article{Albanese2020SpinhAF,
  title={Spin^h and further generalisations of spin},
  author={Michael J. Albanese and Aleksandar Milivojevi{\'c}},
  journal={arXiv: Algebraic Topology},
  year={2020}
}
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 orientable manifold of dimension 7 and lower is spin^h, and that there are orientable manifolds which are not spin^h in all higher… Expand

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