-regular embeddings of the plane

Authors:
F. R. Cohen and D. Handel

Journal:
Proc. Amer. Math. Soc. **72** (1978), 201-204

MSC:
Primary 57-XX

DOI:
https://doi.org/10.1090/S0002-9939-1978-0524347-1

MathSciNet review:
524347

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Abstract: A map is said to be *k*-regular if whenever are distinct points of *X*, then are linearly independent. Such maps are of interest in the theory of Cebyšev approximation. In this paper, configuration spaces and homological methods are used to show that there does not exist a *k*-regular map of into where denotes the number of ones in the dyadic expansion of *k*. This result is best possible when *k* is a power of 2.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0524347-1

Keywords:
*k*-regular maps,
configuration spaces,
Dyer-Lashof operations,
Stiefel-Whitney classes

Article copyright:
© Copyright 1978
American Mathematical Society