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res:
bibo_abstract:
- 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 Sn, there
exists an Sn-equivariant map X→Rn whose image avoids the diagonal {(x,x,…,x)∈Rn∣x∈R}.
Previously, the special cases of this statement for certain X were usually proved
using the equivartiant obstruction theory. Such calculations are difficult and
may become infeasible past the first (primary) obstruction. We take a different
approach which allows us to prove the vanishing of all obstructions simultaneously.
The essential step in the proof is classifying the possible degrees of Sn-equivariant
maps from the boundary ∂Δn−1 of (n−1)-simplex to itself. Existence of equivariant
maps between spaces is important for many questions arising from discrete mathematics
and geometry, such as Kneser’s conjecture, the Square Peg conjecture, the Splitting
Necklace problem, and the Topological Tverberg conjecture, etc. We demonstrate
the utility of our result applying it to one such question, a specific instance
of envy-free division problem.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Sergey
foaf_name: Avvakumov, Sergey
foaf_surname: Avvakumov
foaf_workInfoHomepage: http://www.librecat.org/personId=3827DAC8-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Sergey
foaf_name: Kudrya, Sergey
foaf_surname: Kudrya
foaf_workInfoHomepage: http://www.librecat.org/personId=ecf01965-d252-11ea-95a5-8ada5f6c6a67
bibo_doi: 10.1007/s00454-021-00299-z
bibo_issue: '3'
bibo_volume: 66
dct_date: 2021^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0179-5376
- http://id.crossref.org/issn/1432-0444
dct_language: eng
dct_publisher: Springer Nature@
dct_subject:
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Theoretical Computer Science
dct_title: Vanishing of all equivariant obstructions and the mapping degree@
...