4 problems

Let $p$ be a prime, let $n_1,\ldots,n_k$ be positive integers, and let $L_p^{2n_i-1}$ denote the corresponding lens spaces. Allday's conjecture. The free $p$-rank of their product…

Let $p$ be a prime, let $n_1,\ldots,n_k$ be positive integers, and let $(\mathbb{Z}_p)^r$ act freely on the product $S^{n_1}\times\cdots\times S^{n_k}$. Free-rank conjecture for pr…

Let $\mu:\mathbb{N}\to\{0,1\}$ be defined by … Let $X$ be a finite-dimensional CW-complex homotopy equivalent to $\prod_{i=1}^k S^{m_i}\times\mathbb{C}P^{n_i}$, with each $m_i>0$,…

Let $n_1,\ldots,n_k$ be natural numbers, and define … Suppose $(\mathbb{Z}_2)^r$ acts freely and mod $2$ cohomologically trivially on…