2 problems

Let $\Gamma<\operatorname{Isom}(\mathbb{R}^k)$ be a torsion-free crystallographic group. Its quotient $\mathbb{R}^k/\Gamma$ is a closed aspherical manifold, and…

Let $M^g$ be a Riemann surface of genus $g$, let $\pi_1 M$ be its fundamental group, and let $K^{\mathrm{def}}(\pi_1 M)$ denote the deformation $K$-theory spectrum of this group. L…