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In the following paper " On actions of $SO(3)$ on lens spaces II" by S. Kim and J. Pak the following result (Lemma 1.1) has been used Any effective action of $SO(3)$ on $L_{2n+1}(m)$, $m$ odd can …

In Spanier's book " Algebraic topology" a fiber bundle is defined as follows: A fiber bundle $\xi=(E,B,F,p)$ consists of a total space $E$, a base space $B$ and a fiber $F$ and a bundle projection $p …

Let $G$ be a compact Lie group acting freely on $X\times Y$ , product of two Hausdorff spaces. Is is true that $G$ must act freely on one of the factor spaces ($X$ or $Y$). For example the group $\mat …

It is well known that the group $G=\mathbb Z_2\oplus\mathbb Z_2$ cannot act freely on mod 2 cohomology n-sphere. Is it also true that this group $G$ cannot act freely on any mod p cohomology n-spher …

Let the group $G=\mathbb S^3$ act semi freely on a paracompact space $X$. Then exercise 12 of G.E. Breadon's book , Introduction to compact transformation groups pg 169 asks to derive the following ex …