Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Author(s)

Marzantowicz, Waclaw ^[1] ; de Mattos, Denise ^[2] ; dos Santos, Edivaldo L. ^[2]

Affiliation

^[1] Adam Mickiewicz Univ, Fac Math & Comp Sci, PL-61614 Poznan - Poland

^[2] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Algebraic and Geometric Topology; v. 12, n. 4, p. 2245-2258, 2012.
• Web of Science Citations: 1

Abstract

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = [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 f(-1)[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'. (AU)

• FAPESP's process: 11/18761-2 - An estimate of the dimension of counter-image of $Z_{p^k}$- equivariant mapping between spheres of representations
• Grantee: Edivaldo Lopes dos Santos
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 11/18758-1 - Equivariant mini-max theories, ring-valued genus, and the Borsuk-Ulam theorems
• Grantee: Denise de Mattos
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 10/51910-9 - Waclaw Boleslaw Marzantowicz | Adam Mickiewicz University - Poland
• Grantee: Denise de Mattos
• Support Opportunities: Research Grants - Visiting Researcher Grant - International