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Homology sphere - Wikipedia
The Poincaré homology sphere (also known as Poincaré dodecahedral space) is a particular example of a homology sphere, first constructed by Henri Poincaré. Being a spherical 3-manifold, it is the only homology 3-sphere (besides the 3-sphere itself) with a finite fundamental group. Its fundamental group is known … See more
In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer $${\displaystyle n\geq 1}$$. That is,
and See more• The Rokhlin invariant is a $${\displaystyle \mathbb {Z} /2\mathbb {Z} }$$-valued invariant of homology 3-spheres.
• The See more• A 16-Vertex Triangulation of the Poincaré Homology 3-Sphere and Non-PL Spheres with Few Vertices by Anders Björner and Frank H. Lutz
• Lecture by David Gillman on The best picture of Poincare's homology sphere See moreIf A is a homology 3-sphere not homeomorphic to the standard 3-sphere, then the suspension of A is an example of a 4-dimensional See more
• Dror, Emmanuel (1973). "Homology spheres". Israel Journal of Mathematics. 15 (2): 115–129. doi:10.1007/BF02764597. MR 0328926. S2CID 189796498.
• Galewski, … See moreWikipedia text under CC-BY-SA license - An important class of manifolds called Brieskorn manifolds are obtained as links of Brieskorn singularities. These include the Poincare homology sphere. These also have descriptions as Seifert manifolds.
Invariants of Homology 3-Spheres | SpringerLink
Homology 3-sphere is a closed 3-dimensional manifold whose homology equals that of the 3-sphere. These objects may look rather special but they have played an outstanding role in geometric topology for the past fifty years.
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Homology 3-Spheres | SpringerLink
Let R be a commutative ring with an identity element. By an R-homology 3-sphere we will mean a closed oriented 3-manifold M such that H * (M, R) = H * (S 3, R). In dimension three, the …
- Author: Nikolai Saveliev
- Publish Year: 2002
Every homology 3-sphere can be represented as a framed link, in the sense of Kirby, of the following special type. There are k disjoint embeddings in Ss of a genus one surface with two …
We study 3-manifolds that are homology 3-spheres and which ad-mit nontrivial regular coverings by homology 3-spheres. Our main theorem establishes a relationship between such coverings …
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1Homology 3-Spheres Let R be a commutative ring with. an identity elem. nt. By an R-homology 3-sphere w will mean aclosed oriented 3-manifold M such that H. (M, R) = H, (83, R). In …
Assum-ing certain conjectures in number theory, we show that there exist hyperbolic rational homology 3–spheres with arbitrarily large injectivity radius. These examples come from a …
eriodic cohomology of period two or four. Those which act freely on the standard 3-sphere are the nite fundamental groups of closed 3-manifolds. A basic example of a free action on a rational …
[1605.08530] Integer homology 3-spheres admit irreducible ...
May 27, 2016 · We prove that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL (2,C).
If 2 is any homology three sphere, define T(2) to be the minimum of all the Chern-Simons invariants of non-trivial flat connections in the trivial SO(3)-bundle over 2. We investigate the …
ER Abstract. We use instanton gauge theory to prove that if Y is a closed, orientable 3-manifold such that H1(Y ; Z) is nontrivial and either 2-torsion or 3-torsion, and if Y is neither #rRP3 for …
gt.geometric topology - Classification of homology 3-spheres ...
Jan 23, 2022 · The working description homology 3-spheres for many purposes, in particular quantum topological invariants, is rather different. In practice, a homology 3-sphere is often …
We study 3-manifolds that are homology 3-spheres and which ad-mit nontrivial regular coverings by homology 3-spheres. Our main theorem establishes a relationship between such coverings …
In this paper, we show that rational homology 3-spheres are ubiq-uitous from the viewpoint of Heegaard splitting. Let M = H+ ∪F H− be a genus g Heegaard splitting of a closed 3-manifold …
We study the relationship between trivial cocycles on the Torelli group and invariants of oriented integral homology 3-spheres. We apply this study to give a new purely algebraic construction …
Our goal is to understand how to calculate the Floer homology for the connected sum of two homology 3-spheres. This paper is based on understanding the boundary map for the FΊoer …
We prove that an integral homology 3–sphere is S3 if and only if it admits four periodic diffeomorphisms of odd prime orders whose space of orbits is S3. As an application we show …
homology sphere - PlanetMath.org
Feb 10, 2018 · The original version of the Poincaré conjecture stated that every 3 dimensional homology sphere was homeomorphic to S3 S 3, but Poincaré himself found a counter …
Recently, an analogous theory of nite type invariants of integral homology 3-spheres started to emerge. The analogy is mainly based on the common goal of bringing some order to the …
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