3 problems

Let $d$ be a nonnegative integer, let $(\mathbb{Z}/2\mathbb{Z})^{d}$ be the elementary abelian $2$-group of rank $d$, and let $\mathcal{K}_{d}$ be a Gysin-…

Let $X$ be a finite-dimensional CW complex. Define its rational homological rank by … Let $\mathrm{trk}(X)$ denote the maximal rank of a torus acting almost freely on $X$. The tora…

Let $X$ be a finite-dimensional paracompact Hausdorff space. Suppose that $X$ admits a free action of a torus $T^r$ or a $p$-torus $({\mathbb Z}_p)^r$, where $p$ is prime and the r…