Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Thurston elliptization conjecture
Summary
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 a Riemannian metric of constant positive sectional curvature is covered by the 3-sphere, moreover the group of covering transformations are isometries of the 3-sphere.
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 Poincaré conjecture as a corollary. In fact, the elliptization conjecture is logically equivalent to two simpler conjectures: the Poincaré conjecture and the spherical space form conjecture.
The elliptization conjecture is a special case of Thurston's geometrization conjecture, which was proved in 2003 by G. Perelman.
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related courses (1)
MATH-731: Topics in geometric analysis I
The subject deals with differential geometry and its relation to global analysis, partial differential equations, geometric measure theory and variational principles to name a few.