can you explain to me what the Poincaré conjecture problem is?

Question

i am totaly ignorant of all mathematical concepts and terms.

Answer 1

The Poincare conjecture is a problem in topology, the branch of math that deals with abstract shapes and networks.

In the 3-dimensional world we live in, if you draw a circle anywhere on the surface of a sphere, you can shrink that circle down to a single point. But there is a shape called a torus, which is like a donut or a tire. If you draw a circle on the surface of a torus, you might or might NOT be able to shrink it down to a point -- because you might have drawn the circle all the way around the hole, or all the way around the torus from inside to outside. And that's the topological difference between a sphere and a torus.

That's true for 3-dimensional space.

But is that ALSO true for mathematical spaces of greater than 3 dimensions? Can you also distinguish, say a 4-dimensional sphere from a 4-dimensional torus that same way? Poincare conjectured that it IS also true for all other dimensions. His conjecture has recently been proven true.

Answer 2

In mathematics, the Poincaré conjecture is a conjecture about the characterization of the three-dimensional sphere amongst three-dimensional manifolds. Loosely speaking, the conjecture surmises that if a closed three-dimensional manifold is sufficiently like a sphere in that each loop in the manifold can be tightened to a point, then it is really just a three-dimensional sphere. The analogous result has been known to be true in higher dimensions for some time.

Answer 3

every closed, simply connected 3 manifold can be bicontinously deformed into a 3-sphere.

Answer 4

Yeah, as someone had rightly pointed out, then there is no business for you to ask such a question in the first place .......

Answer 5

Then why do you want to know?