4 problems

Let $Y$ be an aspherical finite $2$-dimensional $CW$-complex, and let $X$ be a connected $CW$-subcomplex of $Y$. Whitehead conjecture. The subcomplex $X$ is aspherical. This conjec…

Let $(Y,y)$ be a finite aspherical CW-complex which is not acyclic, and let $f\colon (X,x)\to (Y,y)$ be a continuous map. Define the degree of $f$ by letting $\deg(f)$ be the least…

Let $M$ be a finite aspherical $CW$-complex (or weakly a closed, connected, oriented and aspherical Riemannian manifold) with fundamental group $\pi$. Write $C_{r}^{\ast }(\pi )$ f…

K(pi,1) conjecture. Such orbit spaces are always $K(\pi,1)$ spaces.