Vanishing of All Equivariant Obstructions and the Mapping Degree

@article{Avvakumov2021VanishingOA,
  title={Vanishing of All Equivariant Obstructions and the Mapping Degree},
  author={Sergey Avvakumov and S. Kudrya},
  journal={Discrete \& Computational Geometry},
  year={2021},
  volume={66},
  pages={1202-1216}
}
Suppose that n is not a prime power and not twice a prime power. We prove that for any Hausdorff compactum X with a free action of the symmetric group  $${\mathfrak {S}}_n$$ S n , there exists an $${\mathfrak {S}}_n$$ S n -equivariant map $$X \rightarrow {{\mathbb {R}}}^n$$ X → R n whose image avoids the diagonal $$\{(x,x,\dots ,x)\in {{\mathbb {R}}}^n\mid x\in {{\mathbb {R}}}\}$$ { ( x , x , ⋯ , x ) ∈ R n ∣ x ∈ R } . Previously, the special cases of this statement for certain X were usually… 

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