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arXiv:0807.0837v1[math.DG]5Jul2008 Topology of Non-simply connected LCF 4-Manifolds

Summary: arXiv:0807.0837v1[math.DG]5Jul2008
Topology of Non-simply connected LCF 4-Manifolds
Selman Akbulut
Mustafa Kalafat
June 26, 2008
We construct handlebody diagrams of families of non-simply connected Locally Con-
formally Flat (LCF) 4-manifolds realizing rich topological types, which are obtained
from conformal compactification of the 3-manifolds, that are built from the Panelled
Web Groups. These manifolds have strictly negative scalar curvature and the underlying
topological 4-manifolds do not admit any Einstein metrics.
1 Introduction
A Riemannian n-manifold (M, g) is called Locally Conformally Flat(LCF) if there is a func-
tion f : U R+ in a neighborhood of each point p M such that
g = fg
is a flat metric in U. It turns out that there is a simple tensorial description of this elaborate
condition. The Weyl curvature tensor is defined as
Wijkl = Rijkl +
(n - 2)(n - 3)


Source: Akbulut, Selman - Department of Mathematics, Michigan State University


Collections: Mathematics