Configuration-like spaces and the Borsuk-Ulam theorem

Cohen, Fred; Lusk, Ewing L.

doi:10.1090/S0002-9939-1976-0425949-1

Configuration-like spaces and the Borsuk-Ulam theorem
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by Fred Cohen and Ewing L. Lusk

Proc. Amer. Math. Soc. 56 (1976), 313-317

DOI: https://doi.org/10.1090/S0002-9939-1976-0425949-1

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Abstract:

Some extensions of the classical Borsuk-Ulam Theorem are proved by computing a bound on the homology of certain spaces similar to configuration spaces. The Bourgin-Yang Theorem and a generalization due to Munkholm are special cases of these results.

References

Drei Sätze über die $n$-dimensional Euklidische Sphäre

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D. G. Bourgin, On some separation and mapping theorems, Comment. Math. Helv. 29 (1955), 199–214. MR 72469, DOI 10.1007/BF02564279
Fred Cohen and J. E. Connett, A coincidence theorem related to the Borsuk-Ulam theorem, Proc. Amer. Math. Soc. 44 (1974), 218–220. MR 331374, DOI 10.1090/S0002-9939-1974-0331374-2
Fred Cohen and Ewing L. Lusk, Coincidence point results for spaces with free $Z_{p}$-actions, Proc. Amer. Math. Soc. 49 (1975), 245–252. MR 372846, DOI 10.1090/S0002-9939-1975-0372846-5
Edward Fadell and Lee Neuwirth, Configuration spaces, Math. Scand. 10 (1962), 111–118. MR 141126, DOI 10.7146/math.scand.a-10517
Hans Jørgen Munkholm, Borsuk-Ulam type theorems for proper $Z_{p}$-actions on ($\textrm {mod}$ $p$ homology) $n$-spheres, Math. Scand. 24 (1969), 167–185 (1970). MR 258025, DOI 10.7146/math.scand.a-10928
Chung-Tao Yang, Continuous functions from spheres to euclidean spaces, Ann. of Math. (2) 62 (1955), 284–292. MR 0072471, DOI 10.2307/1969682