Fundamental polyhedra for Margulis space-times (Q1209377)

Complete affinely flat manifolds correspond to subgroups \(\Gamma\subset\text{Aff}(\mathbb{R}^ n)\) which act properly discontinuously on \(\mathbb{R}^ n\) and \(\pi_ 1(M)\cong\Gamma\) for \(M=\mathbb{R}^ n/\Gamma\) [\textit{J. M. Milnor}, Adv. Math. 25, 178-187 (1977; Zbl 0364.55001)]. Margulis constructed subgroups \(\Gamma\subset\text{Aff}(\mathbb{R}^ 3)\) acting freely and properly discontinuously on \(\mathbb{R}^ 3\) such that \(\Gamma\cong\pi_ 1(\mathbb{R}^ 3/\Gamma)\), and the underlying linear group of each \(\Gamma\) is conjugate to a subgroup of \(\text{SO}^ 0(2,1)\). See e.g. [\textit{G. A. Margulis}, J. Sov. Math. 134, 129-134 (1987); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 134, 190-205 (1984; Zbl 0547.57030); \textit{D. Fried} and \textit{W. M. Goldman}, Adv. Math. 47, 1-49 (1983; Zbl 0571.57030)]. The author constructed fundamental polyhedra for these, so-called, Margulis space-times, which are non-compact and conjectured to have the topological type of a solid handlebody of genus \(n\), if \(\Gamma\) has \(n\) generators.