Abstract
Let be a cyclic group of prime power order and let and be orthogonal representations of with . Let be the sphere of and suppose is a –equivariant mapping. We give an estimate for the dimension of the set in terms of and . 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 –coincidences set of a continuous map from into a real vector space .
Citation
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
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