Mathematics – Geometric Topology
Scientific paper
2005-10-05
Mathematics
Geometric Topology
10 pages
Scientific paper
It is proved that for a product action of $(\mathbb Z_p)^k$ on a product of (mod p) homology spheres $N^{n_1}\times...\times N^{n_k}$, where all $n_i$'s are assumed to be odd if $p$ is odd, and any continuous map $f\colon N^{n_1}\times...\times N^{n_k}\to \mathbb R^m$ the set $A(f)=\{x\in N^{n_1}\times...\times N^{n_k}| f(x)=f(gx) \forall g\in(\mathbb Z_p)^k\}$ has dimension at least $n_1+...+n_k-m(p^k-1)$, provided $n_i\ge mp^{i-1}(p-1)$ for all $i (1\le i\le k)$. Moreover, if $n_i\ge mp^{k-1}(p-1)$ for all $i(1\le i\le k)$ then the free action $\mu$ can be assumed arbitrary.
No associations
LandOfFree
A Borsuk-Ulam theorem for $(\mathbb Z_p)^k$-actions on products of (mod $p$) homology spheres does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Borsuk-Ulam theorem for $(\mathbb Z_p)^k$-actions on products of (mod $p$) homology spheres, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Borsuk-Ulam theorem for $(\mathbb Z_p)^k$-actions on products of (mod $p$) homology spheres will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-250282