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Proceedings of the American Mathematical Society

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

 

 

$ k$-regular mappings of $ 2\sp{n}$-dimensional Euclidean space


Author: Michael E. Chisholm
Journal: Proc. Amer. Math. Soc. 74 (1979), 187-190
MSC: Primary 55S99; Secondary 41A50
DOI: https://doi.org/10.1090/S0002-9939-1979-0521896-8
MathSciNet review: 521896
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Abstract: A map $ f:X \to {R^n}$ is said to be k-regular if whenever $ {x_1}, \ldots ,{x_k}$ are distinct points of X, then $ f({x_1}), \ldots ,f({x_k})$ are linearly independent. Using configuration spaces and homological methods, it is shown that there does not exist a k-regular map from $ {R^n}$ into $ {R^{n(k - \alpha (k)) + \alpha (k) - 1}}$ where $ \alpha (k)$ denotes the number of ones in the dyadic expansion of k and n is a power of 2.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0521896-8
Keywords: k-regular maps, configuration spaces, Dyer-Lashof operations, Stiefel-Whitney classes
Article copyright: © Copyright 1979 American Mathematical Society