じゃあこれ解いてみ
Consider a compact 3-dimensional manifold V without boundary.
Is it possible that the fundamental group of V could be trivial, even though V is not homeomorphic to the 3-dimensional sphere?
Poincaré never declared whether he believed this additional condition would characterize the 3-sphere,
but nonetheless, the statement that it does is known as the Poincaré conjecture. Here is the standard form of the conjecture:
Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.
Note that "closed" here means, as customary in this area, the condition of being compact in terms of set topology,
and also without boundary (3-dimensional Euclidean space is an example of a simply connected 3-manifold not homeomorphic to the 3-sphere;
but it is not compact and therefore not a counter-example).
