Poincare's conjecture and the homeotopy group of a closed, orientable 2-manifold
1974 ◽
Vol 17
(2)
◽
pp. 214-221
◽
Keyword(s):
In 1904 Poincaré [11] conjectured that every compact, simply-connected closed 3-dimensional manifold is homeomorphic to a 3-sphere. The corresponding result for dimension 2 is classical; for dimension ≧ 5 it was proved by Smale [12] and Stallings [13], but for dimensions 3 and 4 the question remains open. It has been discovered in recent years that the 3-dimensional Poincaré conjecture could be reformulated in purely algebraic terms [6, 10, 14, 15] however the algebraic problems which are posed in the references cited above have not, to date, proved tractable.
1968 ◽
Vol 64
(3)
◽
pp. 599-602
◽
Keyword(s):
1990 ◽
Vol 118
◽
pp. 99-110
◽
Keyword(s):
2013 ◽
Vol 15
(03)
◽
pp. 1350007
Keyword(s):
2019 ◽
Vol 66
◽
pp. 212-230
◽
Keyword(s):
Keyword(s):
1987 ◽
Vol 43
(2)
◽
pp. 231-245