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december 2017 Equivariant maps between representation spheres
Zbigniew Błaszczyk, Wacław Marzantowicz, Mahender Singh
Bull. Belg. Math. Soc. Simon Stevin 24(4): 621-630 (december 2017). DOI: 10.36045/bbms/1515035011

Abstract

Let $G$ be a compact Lie group. We prove that if $V$ and $W$ are orthogonal $G$-representations such that $V^G=W^G=\{0\}$, then a $G$-equivariant map $S(V) \to S(W)$ exists provided that $\dim V^H \leq \dim W^H$ for any closed subgroup $H\subseteq G$. This result is complemented by a reinterpretation in terms of divisibility of certain Euler classes when $G$ is a torus.

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Zbigniew Błaszczyk. Wacław Marzantowicz. Mahender Singh. "Equivariant maps between representation spheres." Bull. Belg. Math. Soc. Simon Stevin 24 (4) 621 - 630, december 2017. https://doi.org/10.36045/bbms/1515035011

Information

Published: december 2017
First available in Project Euclid: 4 January 2018

zbMATH: 06848705
MathSciNet: MR3743266
Digital Object Identifier: 10.36045/bbms/1515035011

Subjects:
Primary: 55S37
Secondary: ‎55M20, 55N91, 55S35

Rights: Copyright © 2017 The Belgian Mathematical Society

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Vol.24 • No. 4 • december 2017
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