COBORDISM OBSTRUCTIONS TO INDEPENDENT VECTOR FIELDS

@article{Bokstedt2012COBORDISMOT,
  title={COBORDISM OBSTRUCTIONS TO INDEPENDENT VECTOR FIELDS},
  author={Marcel Bokstedt and Johan Louis Dupont and Anne Marie Svane},
  journal={Quarterly Journal of Mathematics},
  year={2012},
  volume={66},
  pages={13-61}
}
We define an invariant for the existence of r pointwise linearly independent sections in the tangent bundle of a closed manifold. For low values of r, explicit computations of the homotopy groups of certain Thom spectra combined with classical obstruction theory identifies this invariant as the top obstruction to the existence of the desired sections. In particular, this shows that the top obstruction is an invariant of the underlying manifold in these cases, which is not true in general. The… 
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