Description

• Title:
  Bisection of measures on spheres and a fixed point theorem
• Creator:
  Crabb, Michael C.
• Description:
  We establish a variant for spheres of results obtained in \cite{HK}, \cite{BBK} 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 \cite{HK}. 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 \cite{HK}, \cite{BBK}.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2021.06.07
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 59, No 2A (June 2022); 537 - 552;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/34359/29096 ;https://apcz.umk.pl/TMNA/article/view/34359/29097
• Subject:
  Euler class;
  symmetric power;
  fixed point;
  involution;
  Primary;
  54H25;
  55M20;
  55M25;
  55R25;
  Secondary;
  51M20;
  55N32
• Identifier: https://apcz.umk.pl/TMNA/article/view/34359
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other