# 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…

## 4 Citations

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- MathematicsArXiv
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This proof is based on generalizations of the Mabillard-Wagner theorem on construction of almost $r$-embeddings from equivariant maps, and of the Ozaydin theorem on existence of equivariants maps.

### ENVY‐FREE DIVISION USING MAPPING DEGREE

- MathematicsMathematika
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In this paper we study envy-free division problems. The classical approach to some of such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and finding…

### Topological methods in geometry and discrete mathematics

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We present solutions to several problems originating from geometry and discrete mathematics: existence of equipartitions, maps without Tverberg multiple points, and inscribing quadrilaterals.…

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. Let G be a ﬁnite group and V a ﬁnite dimensional (non-zero) orthogonal G -module such that, for each prime p dividing the order of G , the subspace of V ﬁxed by a Sylow p -subgroup of G is non-zero…

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