Gottlieb's centralizer conjecture for nonzero-degree maps

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 integer $n\in\mathbb{N}$ for which there exists a group homomorphism

$$\tau\colon H_*(Y,\mathbb{Z})\to H_*(X,\mathbb{Z})$$

with $f_*\circ\tau=n\cdot\operatorname{id}$. Gottlieb's conjecture. If $\deg(f)\neq 0$ and $\chi(Y)\neq 0$, then the centralizer of $f_*(\pi_1(X,x))$ in $\pi_1(Y,y)$ is trivial. The conjecture concerns restrictions on nonzero-degree maps to finite aspherical complexes; the paper's abstract states that it gives a counterexample to the original conjecture and proves a strengthened version, so the original claim is refuted.