Poincaré's Conjecture Proven in 2003

H.-D. CAO AND X.-P. ZHU; state Poincare's Conjecture this way:

"A closed three-manifold with trivial fundamental group is necessarily homeomorphic to the 3-sphere S³"

This result was established more than a hundred years after it was conjectured by Henri Poincaré.

In the end the proof depends on ideas close to what is called the Renormalization Group; the language is Differential Geometry, the arena is Topology.

I was always impressed by the ideas of the seventies in the last century, from Statistical Mechanics, that led to the revolution in phase transition theory. Near the critical point, classes of interactions were equivalent, the correlation lengths become infinite, and after the transition point a new world awaits us.

It is very intriguing to me how does this relate to Poincaré's conjecture.

Now I am beginning to study this deep connection.