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See all on WikipediaHomology 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.
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
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gt.geometric topology - Classification of homology 3-spheres ...
Jan 23, 2022 · There's a general description of all compact 3-manifolds now that geometrization is about. So for homology 3-sphere's you have the essentially unique connect sum …
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.
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 …
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1 Homology 3-Spheres 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, (83 , R). In …
[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). For …
Title: Monopole Floer homology for rational homology 3-spheres
Sep 29, 2008 · We give a new construction of monopole Floer homology for spin-c rational homology 3-spheres. As applications we define two invariants of certain smooth compact 4 …
It is the purpose of this paper to use this set of generators to obtain a representation theorem for all homology 3-spheres as special framed links. It turns out that the formula for the /^-invariant …
Poincaré's homology sphere - Manifold Atlas
Poincaré's homology sphere is a closed 3- manifold with the same homology as the 3-sphere but with a fundamental group which is non-trivial. In his series of papers on Analysis situs (1892 - 1904) Poincaré introduced the fundamental …
In § 3 we compute the instanton index SF(0, a) for representations of Seifert-fibred homology spheres and prove that it is always even, so that the differential of the instanton complex is …
FREE FINITE GROUP ACTIONS ON RATIONAL HOMOLOGY 3{SPHERES ALEJANDRO ADEM AND IAN HAMBLETON Abstract. We use methods from the cohomology of groups to describe …
We will explain how complex hypersurface singularities give rise to knots and links, some of which are manifolds that are homologically spheres but not topologically (Poincare homology …
RATIONAL HOMOLOGY 3-SPHERES AND SL(2;C) REPRESENTATIONS SUDIPTA GHOSH, STEVEN SIVEK, AND RAPHAEL ZENTNER Abstract. We use instanton gauge theory to …
FΊoer homology is a mod 8-graded homology theory for integral ho-mology 3-spheres Y [8]. "The FΊoer" chain groups C^(Y) are generated by irreducible SU(2)-representations of the …
In this paper we will give a general framework to construct invariants of homology spheres in a purely algebraic setting as functions out of the full Torelli group. We will show that the …
Invariants of $\mathbb {Z}/p$-homology 3-spheres from the ...
We study the relation between the set of oriented Z / d-homology 3-spheres and the level-d mapping class groups, the kernels of the canonical maps from the mapping class group of an …
Trivial cocycles and invariants of homology 3-spheres
Jan 15, 2009 · In this paper we will give a general framework to construct invariants of homology spheres in a purely algebraic setting as functions out of the full Torelli group. We will show that …
general topology - Homotopy groups of integer homology 3 …
Sep 14, 2017 · Let $Y^3$ be a integer homology 3-sphere, i.e. $H_k(Y;\mathbb{Z}) = H_k(S^3;\mathbb{Z}), \forall k$, i.e. $$ H_0(Y;\mathbb{Z}) = H_3(Y;\mathbb{Z}) = \mathbb{Z} …
Rapid traversal of vast chemical space using machine learning …
6 days ago · One hundred homology models of the activated D 2 R bound to agonist ligand (PD128907) were constructed using MODELLER 56 version 10.2 based on a cryo-EM …
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