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$2k$-regular maps on smooth manifolds


Author: David Handel
Journal: Proc. Amer. Math. Soc. 124 (1996), 1609-1613
MSC (1991): Primary 57N75, 57R20, 57S17; Secondary 41A50
DOI: https://doi.org/10.1090/S0002-9939-96-03179-6
MathSciNet review: 1307524
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Abstract: A continuous map $f:X\to \mathbf R ^{N}$ is said to be $k$-regular if whenever $x_{1},\dots , x_{k}$ are distinct points of $X$, then $f(x_{1}),\dots , f(x_{k})$ are linearly independent over $\mathbf R $. For smooth manifolds $M$ we obtain new lower bounds on the minimum $N$ for which a $2k$-regular map $M \to \mathbf R ^{N}$ can exist in terms of the dual Stiefel-Whitney classes of $M$.


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Additional Information

David Handel
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: handel@math.wayne.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03179-6
Keywords: $k$-regular maps, configuration spaces, smooth manifolds, dual Stiefel-Whitney classes
Received by editor(s): September 6, 1994
Received by editor(s) in revised form: November 1, 1994
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1996 American Mathematical Society

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