2005/10/05 by Turygin, Yuri A.
#55M10 #55M35 #57S17 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.math/0510086
It is proved that for a product action of (\mathbb Zp)k on a product of (mod p) homology spheres Nn1×...× Nnk, where all ni's are assumed to be odd if p is odd, and any continuous map f\colon Nn1×...× Nnk→ \mathbb Rm the set A(f)=\x∈ Nn1×...× Nnk| f(x)=f(gx) ∀ g∈(\mathbb Zp)k\ has dimension at least n1+...+nk-m(pk-1), provided ni≥ mpi-1(p-1) for all i (1≤ i≤ k). Moreover, if ni≥ mpk-1(p-1) for all i(1≤ i≤ k) then the free action μ can be assumed arbitrary.