Poincaré conjecture

Recent progress on the Poincaré conjecture and the classification of 3-manifolds.

The Poincaré Conjecture is but a small part of that.

An important mathematics open problem solved in early 21st century is the Poincaré conjecture.

From the early 1960s on, he mostly worked on the Poincaré conjecture.

This shows the Poincaré conjecture cannot be stated in homology terms alone.

In the special case when the form is 0, this implies the 4-dimensional topological Poincaré conjecture.

The Poincaré conjecture, before being proven, was one of the most important open questions in topology.

This so-called smooth Poincaré conjecture, in dimension four, remains open and is thought to be very difficult.

He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics.

The Poincaré conjecture was essentially true in both dimension four and all higher dimensions for substantially different reasons.

The Poincaré Conjecture is a question about spheres in mathematics.

Bing also described some of the pitfalls in trying to prove the Poincaré conjecture.

Similarly, differentiable 4-manifolds is the only remaining open case of the generalized Poincaré conjecture.

In 2002 Dunwoody put forward a proposed proof of the Poincaré conjecture.

The Poincaré conjecture is the only solved Millennium problem.

He created the Poincaré Conjecture, one of the most famous problems in mathematics which was only solved 100 years later.

Only the Poincaré conjecture has been solved.

The generalized Poincaré conjecture in dimension can be phrased as saying that .

The Poincaré conjecture is that this is also true for spheres with three-dimensional surfaces.

Michael Freedman proves the Poincaré conjecture in dimensions equal to 4.

For a start, it almost immediately proves the Generalized Poincaré Conjecture.

Stephen Smale proves the Poincaré conjecture in dimensions greater than 4.

The proof (the Solution of the Poincaré conjecture) is analytic, not topological.

Here is a summary of the status of the Generalized Poincaré conjecture in various settings.

Milnor's exotic spheres show that the smooth Poincaré conjecture is false in dimension seven, for example.