4 problems

Let $\{X_i\}_{i=1}^\infty$ be a family of finite simplicial complexes. The strong NE-equivalence conjecture. There exists an infinite family of finite simplicial complexes…

Let $X$ and $Y$ be finite simplicial complexes. The NE-equivalence conjecture. There exist finite simplicial complexes $X$ and $Y$ having the same simple homotopy type, such that…

Simple homotopy type conjecture. There are constants $\alpha(S)$ and $d(S)$ such that any arithmetic $S$-manifold $M=S/\Gamma$ with volume $\mu(M)$ is homotopically equivalent to a…

Let $K_{\mathcal{P}}$ and $K_{\mathcal{Q}}$ be the standard $2$-dimensional CW-complexes of two finite presentations. Simple homotopy equivalence is generated by collapses and expa…