A stronger Borsuk-Ulam type theorem for proper 𝑍_{𝑝}-actions on 𝑚𝑜𝑑𝑝 homology 𝑛-spheres

Roberts, Jean E.

doi:10.1090/S0002-9939-1978-0507343-X

A stronger Borsuk-Ulam type theorem for proper $Z_{p}$-actions on $\textrm {mod}\ p$ homology $n$-spheres
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Proc. Amer. Math. Soc. 72 (1978), 381-386 Request permission

Abstract:

We obtain under a less restrictive hypothesis a Borsuk-Ulam type result of Munkholm’s in which the antipodal map is replaced by a ${Z_p}$-action on a cohomology n-sphere.

References

D. G. Bourgin, Modern algebraic topology, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1963. MR 0160201
P. E. Conner and E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 33, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1964. MR 0176478
P. E. Conner and E. E. Floyd, Fixed point free involutions and equivariant maps, Bull. Amer. Math. Soc. 66 (1960), 416–441. MR 163310, DOI 10.1090/S0002-9904-1960-10492-2
André Haefliger, Points multiples d’une application et produit cyclique réduit, Amer. J. Math. 83 (1961), 57–70 (French). MR 120655, DOI 10.2307/2372720
Hans Jørgen Munkholm, A Borsuk-Ulam theorem for maps from a sphere to a compact topological manifold, Illinois J. Math. 13 (1969), 116–124. MR 238324
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
N. E. Steenrod, Cohomology operations, Annals of Mathematics Studies, No. 50, Princeton University Press, Princeton, N.J., 1962. Lectures by N. E. Steenrod written and revised by D. B. A. Epstein. MR 0145525
Wen-tsün Wu, Classes caractéristiques et $i$-carrés d’une variété, C. R. Acad. Sci. Paris 230 (1950), 508–511 (French). MR 35992
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