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2012 Bourgin–Yang version of the Borsuk–Ulam theorem for $\mathbb{Z}_{p^k}$–equivariant maps
Wacław Marzantowicz, Denise de Mattos, Edivaldo dos Santos
Algebr. Geom. Topol. 12(4): 2245-2258 (2012). DOI: 10.2140/agt.2012.12.2245

Abstract

Let G=pk be a cyclic group of prime power order and let V and W be orthogonal representations of G with VG=WG={0}. Let S(V) be the sphere of V and suppose f:S(V)W is a G–equivariant mapping. We give an estimate for the dimension of the set f1{0} in terms of V and W. This extends the Bourgin–Yang version of the Borsuk–Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G–coincidences set of a continuous map from S(V) into a real vector space W.

Citation

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Wacław Marzantowicz. Denise de Mattos. Edivaldo dos Santos. "Bourgin–Yang version of the Borsuk–Ulam theorem for $\mathbb{Z}_{p^k}$–equivariant maps." Algebr. Geom. Topol. 12 (4) 2245 - 2258, 2012. https://doi.org/10.2140/agt.2012.12.2245

Information

Received: 30 April 2012; Revised: 14 August 2012; Accepted: 27 August 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1262.55001
MathSciNet: MR3020205
Digital Object Identifier: 10.2140/agt.2012.12.2245

Subjects:
Primary: ‎55M20
Secondary: 55M35, 55N91, 57S17

Rights: Copyright © 2012 Mathematical Sciences Publishers

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