Poincaré Conjecture
A Simply Connected 3-Manifold is Homeomorphic to the 3-Sphere. The generalized Poincaréconjecture is that a Compact 
-Manifold is Homotopy equivalent to the -sphereIff it is Homeomorphic to the -Sphere. This reduces to the original conjecture for 
.
The 
case of the generalized conjecture is trivial, the 
case is classical, remains open, 
was proved byFreedman (1982) (for which he was awarded the 1986 Fields Medal), 
by Zeeman (1961), 
by Stallings (1962), and 
by Smale in 1961 (Smale subsequently extended this proof to include 
.)
References
Freedman, M. H. ``The Topology of Four-Differentiable Manifolds.'' J. Diff. Geom. 17, 357-453, 1982. Stallings, J. ``The Piecewise-Linear Structure of Euclidean Space.'' Proc. Cambridge Philos. Soc. 58, 481-488, 1962. Smale, S. ``Generalized Poincaré's Conjecture in Dimensions Greater than Four.'' Ann. Math. 74, 391-406, 1961. Zeeman, E. C. ``The Generalised Poincaré Conjecture.'' Bull. Amer. Math. Soc. 67, 270, 1961. Zeeman, E. C. ``The Poincaré Conjecture for .'' In Topology of 3-Manifolds and Related Topics, Proceedings of the University of Georgia Institute, 1961. Englewood Cliffs, NJ: Prentice-Hall, pp. 198-204, 1961.
- Elliptic Pseudoprime
- Elliptic Rotation
- Elliptic Theta Function
- Elliptic Torus
- Elliptic Umbilic Catastrophe
- Ellison-Mendès-France Constant
- Elongated Cupola
- Elongated Dipyramid
- Elongated Dodecahedron
- Elongated Gyrobicupola
- Elongated Gyrocupolarotunda
- Elongated Orthobicupola
- Elongated Orthobirotunda
- Elongated Orthocupolarotunda
- Elongated Pentagonal Cupola
- Elongated Pentagonal Dipyramid
- Elongated Pentagonal Gyrobicupola
- Elongated Pentagonal Gyrobirotunda
- Elongated Pentagonal Gyrocupolarotunda
- Elongated Pentagonal Orthobicupola
- Elongated Pentagonal Orthobirotunda
- Elongated Pentagonal Orthocupolarotunda
- Elongated Pentagonal Pyramid
- Elongated Pentagonal Rotunda
- Elongated Pyramid