2𝑘-regular maps on smooth manifolds

Handel, David

doi:10.1090/S0002-9939-96-03179-6

$2k$-regular maps on smooth manifolds
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by David Handel PDF

Proc. Amer. Math. Soc. 124 (1996), 1609-1613 Request permission

Abstract:

A continuous map $f:X\to \mathbb {R} ^{N}$ 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 $\mathbb {R}$. For smooth manifolds $M$ we obtain new lower bounds on the minimum $N$ for which a $2k$-regular map $M \to \mathbb {R} ^{N}$ can exist in terms of the dual Stiefel-Whitney classes of $M$.

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