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2021 Bisection of measures on spheres and a fixed point theorem
Michael C. Crabb
Topol. Methods Nonlinear Anal. Advance Publication 1-16 (2021). DOI: 10.12775/TMNA.2020.047

Abstract

We establish a variant for spheres of results obtained in [7], [3] for affine space. The principal result, that, if $m$ is a power of $2$ and $k\geq 1$, then $km$ continuous densities on the unit sphere in $\mathbb R^{m+1}$ may be simultaneously bisected by a set of at most $k$ hyperplanes through the origin, is essentially equivalent to the main theorem of Hubard and Karasev in [7]. But the methods used, involving Euler classes of vector bundles over symmetric powers of real projective spaces and an 'orbifold' fixed point theorem for involutions, are substantially different from those in [7], [3].

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Michael C. Crabb. "Bisection of measures on spheres and a fixed point theorem." Topol. Methods Nonlinear Anal. Advance Publication 1 - 16, 2021. https://doi.org/10.12775/TMNA.2020.047

Information

Published: 2021
First available in Project Euclid: 14 June 2021

Digital Object Identifier: 10.12775/TMNA.2020.047

Keywords: Euler class , fixed point , involution , symmetric power

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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