Finite volume hyperbolic complements of 2-tori and Klein bottles in closed smooth simply connected 4-manifolds
In [\textit{D. Ivanšić}, Adv. Geom. 4, No. 1, 119--139 (2004; Zbl 1039.57012)] an example of a noncompact hyperbolic 4-manifold, under condition of finite volume, is presented that is topologically the complement of 5 tori and Klein bottles in the 4-sphere \(S^4\). \(S^4\) is a closed smooth simply connected 4-manifold and such manifolds are topologically classified. Such a manifold can contain a link of surfaces whose complement admits a complete finite volume hyperbolic structure which forces that the surfaces are either tori or Klein bottles. Assuming the last mentioned condition this author investigates the homeomorphism type of such manifolds obtaining the following three homeomorphism types: {\parindent=6mm \begin{itemize}\item{}\(S^4\); \item{}\(\sharp_k(S^2\times S^2), k>0\); \item{}\(\sharp_k \mathbb CP^2 \sharp_k \overline{\mathbb CP^2}, k>0\). \end{itemize}}
scientific article; zbMATH DE number 6929959