Finite volume hyperbolic complements of 2-tori and Klein bottles in closed smooth simply connected 4-manifolds
type: Item
instance of: scholarly article
title: Finite volume hyperbolic complements of 2-tori and Klein bottles in closed smooth simply connected 4-manifolds
zbMATH Open document ID: 1404.57035
author: Hemanth Saratchandran
published in: The New York Journal of Mathematics
publication date: 2018-08-31T00:00:00Z
full work available at URL: 24-25.html
review text: 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}}
reviewed by: Ivan Ivanšić
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57Q45
zbMATH DE Number: 6929959
zbMATH Keywords: hyperbolic 4-manifolds
zbMATH Keywords: finite volume
zbMATH Keywords: simply connected 4-manifolds
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6929959