Corpus ID: 16414912

Suspensions of homology spheres

@article{Edwards2006SuspensionsOH,
title={Suspensions of homology spheres},
author={Robert D. Edwards},
journal={arXiv: Geometric Topology},
year={2006}
}
• R. Edwards
• Published 2006
• Mathematics
• arXiv: Geometric Topology
This article is one of three highly influential articles on the topology of manifolds written by Robert D. Edwards in the 1970's but never published. It presents the initial solutions of the fabled Double Suspension Conjecture. (The other two articles are: 'Approximating certain cell-like maps by homeomorphisms' and 'Topological regular neighborhoods') The manuscripts of these three articles have circulated privately since their creation. The organizers of the Workshops in Geometric Topology… Expand
32 Citations

Figures from this paper

Algorithmic homeomorphism of 3-manifolds as a corollary of geometrization
In this paper we prove two results, one semi-historical and the other new. The semi-historical result, which goes back to Thurston and Riley, is that the geometrization theorem implies that there isExpand
Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture
We define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. The analogue of Froyshov's correction term in this setting is anExpand
Poincaré conjecture and related statements
The main topics of this paper are mathematical statements, results or problems related with the Poincare conjecture, a recipe to recognize the three-dimensional sphere. The statements, results andExpand
Smoothing discrete Morse theory
After surveying classical notions of PL topology of the Seventies, we clarify the relation between Morse theory and its discretization by Forman. We show that PL handles theory and discrete MorseExpand
Floer theory and its topological applications
We survey the different versions of Floer homology that can be associated to three-manifolds. We also discuss their applications, particularly to questions about surgery, homology cobordism, andExpand
Combinatorial systolic inequalities
• Mathematics
• 2015
We establish combinatorial versions of various classical systolic inequalities. For a smooth triangulation of a closed smooth manifold, the minimal number of edges in a homotopically non-trivial loopExpand
Deformation and quasiregular extension of cubical Alexander maps
• Mathematics
• 2019
In this article we prove that, for an oriented PL $n$-manifold $M$ with $m$ boundary components and $d_0\in \mathbb N$, there exist mutually disjoint closed Euclidean balls and a \$\mathsfExpand
Orientability and fundamental classes of Alexandrov spaces with applications
In the present paper, we consider several valid notions of orientability of Alexandov spaces and prove that all such conditions are equivalent. Further, we give topological and geometric applicationsExpand
Lectures on the triangulation conjecture
We outline the proof that non-triangulable manifolds exist in any dimension greater than four. The arguments involve homology cobordism invariants coming from the Pin(2) symmetry of theExpand
HOMOLOGY COBORDISM AND TRIANGULATIONS
• Ciprian Manolescu
• Mathematics
• Proceedings of the International Congress of Mathematicians (ICM 2018)
• 2019
The study of triangulations on manifolds is closely related to understanding the three-dimensional homology cobordism group. We review here what is known about this group, with an emphasis on theExpand

References

SHOWING 1-10 OF 142 REFERENCES
On the Double Suspension of Certain Homotopy 3-Spheres
In [9] a relationship was noted between the polyhedral Schoenflies problem, and the question of whether the double suspension of a Poincare 3-manifold is the 5-sphere. In [20], it was shown that ifExpand
Foundational Essays on Topological Manifolds, Smoothings, and Triangulations.
• Mathematics
• 1977
Since Poincare's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when KirbyExpand
THE EXISTENCE OF CERTAIN TYPES OF MANIFOLDS
• Mathematics
• 1959
Introduction. The first part of the paper gives a class of polyhedral 3manifolds in the 4-sphere S4 and with homology groups H(M) —H2(M) =0, but with 7ri(M) 5^0. Thus some "Poincare" spaces areExpand
On Homotopy Tori II
• Mathematics
• 1969
In the preprint [2] of Kirby and Siebenmann, it is shown that vanishes for / # 3 and has order at most 2 in that case. It is further shown that isotopy classes of PL structures on a topologicalExpand
Cell-like closed-0-dimensional decompositions of ³ are ⁴ factors
• Mathematics
• 1976
It is proved that the product of a cell-like closed-0dimensional upper semicontinuous decomposition of R3 with a line is R4. This establishes at once this feature for all the various dogbone-inspiredExpand
On Involutions of Spheres
1. R. H. Bing [1] has given an example of an involution of a 3-sphere whose fixed points constitute a wild (horned) 2-sphere. This shows that an involution in a euclidean n-sphere, SO, is notExpand
Smooth homology spheres and their fundamental groups
Let Mn be a smooth homology n-spherei, i.e. a smooth n-dimensional manifold such that H*(Mn) H*(S n). The fundamental group -a of M satisfies the following three conditions: (1) -a has a finiteExpand
Shrinking cell-like decompositions of manifolds. Codimension three
Euclidean n-space En, n > 5, has the following simple DISJOINT DISK PROPERTY: singular 2-dimensional disks in En may be adjusted slightly so as to be disjoint. We show that for a large class ofExpand
Deformation of homeomorphisms on stratified sets
T H E O R E M 0. The topological group H(X) of homeomorphisms of a finite simplicial complex X onto itself is locally contractible. This result does not extend to ENR's (euclidean neighborhoodExpand
On the polyhedral Schoenflies theorem
• Mathematics
• 1960
In this note we observe a relationship between the polyhedral Schoenflies problem and the question of whether the double suspension M" of a Poincare manifold is the 5-sphere. In particular we showExpand