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A note on fixed point free involutions and equivariant maps


Author: Jack Ucci
Journal: Proc. Amer. Math. Soc. 31 (1972), 297-298
MSC: Primary 55C10; Secondary 58E05
DOI: https://doi.org/10.1090/S0002-9939-1972-0298656-2
MathSciNet review: 0298656
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Abstract: The space $ P({S^n})$ of all paths $ \omega $ in $ {S^n}$ with given initial point $ x$ and endpoint $ - x$ admits an involution $ (T\omega )(t) = - \omega (1 - t)$. With the standard antipodal involution on $ {S^{n - 1}}$ an equivariant map $ P({S^n}) \to {S^{n - 1}}$ is constructed for $ n = 2,4,$, or $ 8$.


References [Enhancements On Off] (What's this?)

  • [1] K. Borsuk, Drei Sätze über die $ n$-dimensionale euklidische Sphäre, Fund. Math. 20 (1933), 177-190.
  • [2] P. E. Conner and E. E. Floyd, Fixed point free involutions and equivariant maps. II, Trans. Amer. Math. Soc. 105 (1962), 222-228. MR 26 #768. MR 0143208 (26:768)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0298656-2
Keywords: Fixed point free involution, equivariant map, co-index
Article copyright: © Copyright 1972 American Mathematical Society

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