Bulletin of the Belgian Mathematical Society - Simon Stevin

Equivariant maps between representation spheres

Zbigniew Błaszczyk, Wacław Marzantowicz, and Mahender Singh

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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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 4 (2017), 621-630.

Dates
First available in Project Euclid: 4 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1515035011

Digital Object Identifier
doi:10.36045/bbms/1515035011

Mathematical Reviews number (MathSciNet)
MR3743266

Zentralblatt MATH identifier
06848705

Subjects
Primary: 55S37: Classification of mappings
Secondary: 55M20: Fixed points and coincidences [See also 54H25] 55S35: Obstruction theory 55N91: Equivariant homology and cohomology [See also 19L47]

Keywords
Borsuk--Ulam theorem equivariant map Euler class representation sphere

Citation

Błaszczyk, Zbigniew; Marzantowicz, Wacław; Singh, Mahender. Equivariant maps between representation spheres. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 4, 621--630. doi:10.36045/bbms/1515035011. https://projecteuclid.org/euclid.bbms/1515035011


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