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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Antipodal coincidence for maps of spheres into complexes
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by Marek Izydorek and Jan Jaworowski PDF
Proc. Amer. Math. Soc. 123 (1995), 1947-1950 Request permission

Abstract:

This paper gives a partial answer to the question of whether there exists a Borsuk-Ulam type theorem for maps of ${S^n}$ into lower-dimensional spaces, which are not necessarily manifolds. It is shown that for each k and $n \leq 2k - 1$, there exists a map f of ${S^n}$ into a contractible k-dimensional complex Y such that $fx \ne f( - x)$, for all $x \in {S^n}$. In particular, there exists a map of ${S^3}$ into a 2-dimensional complex Y without an antipodal coincidence. This answers a question raised by Conner and Floyd in 1964. The complex Y provides also an example of a countractible k-dimensional complex whose deleted product has the Yang-index equal to $2k - 1$.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1947-1950
  • MSC: Primary 55M20; Secondary 55M35
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1242089-4
  • MathSciNet review: 1242089