Объясните плз по простому доказательство гипотизы Пуанкаре? что это вообще такое?

Вот аннотация оригинала читай:
This is a technical paper, which is a continuation of . Here we verify most
of the assertions, made in [I, §13]; the exceptions are (1) the statement that a
3-manifold which collapses with local lower bound for sectional curvature is a
graph manifold - this is deferred to a separate paper, as the proof has nothing to
do with the Ricci flow, and (2) the claim about the lower bound for the volumes
of the maximal horns and the smoothness of the solution from some time on,
which turned out to be unjustified, and, on the other hand, irrelevant for the
other conclusions.
The Ricci flow with surgery was considered by Hamilton [H 5,§4,5]; unfortunately,
his argument, as written, contains an unjustified statement (RMAX = 􀀀,
on page 62, lines 7-10 from the bottom), which I was unable to fix. Our approach
is somewhat different, and is aimed at eventually constructing a canonical Ricci
flow, defined on a largest possible subset of space-time, - a goal, that has not
been achieved yet in the present work. For this reason, we consider two scale
bounds: the cutoff radius h, which is the radius of the necks, where the surgeries
are performed, and the much larger radius r, such that the solution on the
scales less than r has standard geometry. The point is to make h arbitrarily
small while keeping r bounded away from zero.