Topic
Exotic sphere
About: Exotic sphere is a research topic. Over the lifetime, 153 publications have been published within this topic receiving 6222 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, the disjoint sum of two connected n-manifolds is obtained by removing a small n-cell from each, and then pasting together the resulting boundaries.
Abstract: DEFINITION. Two closed n-manifolds M, and M2 are h-cobordant1 if the disjoint sum M, + (- M2) is the boundary of some manifold W, where both M1 and (-M2) are deformation retracts of W. It is clear that this is an equivalence relation. The connected sum of two connected n-manifolds is obtained by removing a small n-cell from each, and then pasting together the resulting boundaries. Details will be given in ? 2.
1,017 citations
Journal Article•
684 citations
631 citations
TL;DR: The generalized Poincare conjecture as discussed by the authors states that every simply connected closed 3-manifold is homeomorphic to the 3-sphere if n > 5 and for differentiable manifolds in the following theorem and combinatorial manifold in Theorem B.
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).
517 citations
TL;DR: In this article, it was shown that the Kervaire invariant one elements θj ∈ π2j+1−2S exist only for j ≤ 6.
Abstract: We show that the Kervaire invariant one elements θj ∈ π2j+1−2S exist only for j ≤ 6. By Browder’s Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14, 30, 62, and possibly 126. Except for dimension 126 this resolves a longstanding problem in algebraic topology.
472 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 4 |
| 2020 | 11 |
| 2019 | 3 |
| 2018 | 4 |
| 2017 | 5 |
| 2016 | 9 |