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Generalized Poincare's Conjecture in Dimensions Greater Than Four
Abstract
Poincare has posed the problem as to whether every simply connected closed 3-manifold (triangulated) is homeomorphic to the 3-sphere, see [18] for example. This problem, still open, is usually called Poincare's conjecture. The generalized Poincare conjecture (see [11] or [28] for example) says that every closed n-manifold which has the homotopy type of the nsphere S is homeomorphic to the n-sphere. One object of this paper is to prove that this is indeed the case if n > 5 (for differentiable manifolds in the following theorem and combinatorial manifolds in Theorem B).
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Cites
Kervaire, M. A., & Milnor, J. W. (1963) · The Annals of Mathematics · doi:10.2307/1970128 · Cited by 904
Cited by
Alvarez-Gaumé, L., & Witten, E. (1984) · Nuclear Physics B · doi:10.1016/0550-3213(84)90066-x · Cited by 1,268
Kervaire, M. A., & Milnor, J. W. (1963) · The Annals of Mathematics · doi:10.2307/1970128 · Cited by 904
Robot navigation functions on manifolds with boundary
Koditschek, D. E., & Rimon, E. (1990) · Advances in Applied Mathematics · doi:10.1016/0196-8858(90)90017-s · Cited by 567
Large sample theory of intrinsic and extrinsic sample means on manifolds
Bhattacharya, R., & Patrangenaru, V. (2003) · The Annals of Statistics · doi:10.1214/aos/1046294456 · Cited by 401
Grove, K., & Shiohama, K. (1977) · The Annals of Mathematics · doi:10.2307/1971164 · Cited by 286
Metadata
- Authors
- Smale, S.
- Venue
- The Annals of Mathematics
- Publisher
- JSTOR
- Published
- 1961-09
- Volume
- 74
- Issue
- 2
- Pages
- 391
- ISSN
- 0003-486X (ISSN-L)
- OpenAlex
- W1980124684
- Cited by
- 428
- References
- 1
- FWCI
- 18.53
- Type
- journal article
- Language
- en
- Open access
- closed
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