thurston elliptization conjecture

William Thurston's Elliptization Conjecture states that a closed 3-manifold with finite fundamental group is spherical, i.e. has a Riemannian metric of constant positive sectional curvature. A 3-manifold with such a metric is covered by the 3-sphere, moreover the group of covering transformations are isometries of the 3-sphere. Note that this means that if the original 3-manifold had in fact a trivial fundamental group, then it is homeomorphic to the 3-sphere (via the covering map). Thus, proving the Elliptization Conjecture would prove the Poincar conjecture as a corollary. In fact, the Elliptization Conjecture is logically equivalent to two simpler conjectures: the Poincare conjecture and the linearization conjecture. The Elliptization Conjecture is a special case of Thurston's Geometrization Conjecture.

<< Previous

Word Browser

Next >>

submersible pump
mechanical seal
short circuit
circuit breaker
overload
johann carl otto ribbeck
borehole
shaft
dimitri tiomkin
culture of sweden
water abstraction

tongling
doggerel
gaius julius solinus
jada pinkett smith
arthur golding
charlotte turner smith
buttermilk
dna polymerase
pomponius mela
topoisomerase
johann friedrich gronovius

raphael fabretti
carrageenan
albert ii, prince of monaco
technology lifecycle
double density
claudius salmasius
grorschen
numerical sight singing
farrah fawcett
philippe de mornay
marcus terentius varro

viljandi
aquila romanus
hydrogenation
aristides quintilianus
tom araya
sarcopterygii
marcus velleius paterculus
stahlhelm, bund der frontsoldaten
bichir
rockwell scale
first lord of the treasury