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Comparison Geometry MSRI Publications

Summary: Comparison Geometry
MSRI Publications
Volume 30, 1997
Scalar Curvature and Geometrization
Conjectures for 3­Manifolds
Abstract. We first summarize very briefly the topology of 3­manifolds
and the approach of Thurston towards their geometrization. After dis­
cussing some general properties of curvature functionals on the space of
metrics, we formulate and discuss three conjectures that imply Thurston's
Geometrization Conjecture for closed oriented 3­manifolds. The final two
sections present evidence for the validity of these conjectures and outline
an approach toward their proof.
In the late seventies and early eighties Thurston proved a number of very re­
markable results on the existence of geometric structures on 3­manifolds. These
results provide strong support for the profound conjecture, formulated by Thur­
ston, that every compact 3­manifold admits a canonical decomposition into do­
mains, each of which has a canonical geometric structure.
For simplicity, we state the conjecture only for closed, oriented 3­manifolds.


Source: Anderson, Michael - Department of Mathematics, SUNY at Stony Brook


Collections: Mathematics