 
Summary: arXiv:0807.0837v1[math.DG]5Jul2008
Topology of Nonsimply connected LCF 4Manifolds
Selman Akbulut
Mustafa Kalafat
June 26, 2008
Abstract
We construct handlebody diagrams of families of nonsimply connected Locally Con
formally Flat (LCF) 4manifolds realizing rich topological types, which are obtained
from conformal compactification of the 3manifolds, that are built from the Panelled
Web Groups. These manifolds have strictly negative scalar curvature and the underlying
topological 4manifolds do not admit any Einstein metrics.
1 Introduction
A Riemannian nmanifold (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 +
R
(n  2)(n  3)
