The Hopf type theorem for equivariant gradient local maps

@article{Bartomiejczyk2015TheHT,
  title={The Hopf type theorem for equivariant gradient local maps},
  author={Piotr Bartłomiejczyk and Piotr Nowak-Przygodzki},
  journal={Journal of Fixed Point Theory and Applications},
  year={2015},
  volume={19},
  pages={2733-2753}
}
We construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of equivariant gradient otopy classes and the direct sum of countably many copies of $$\mathbb {Z}$$Z. 

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