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Invariants• The Rokhlin invariant is a -valued invariant of homology 3-spheres.
• The Casson invariant is an integer valued invariant of homology 3-spheres, whose reduction mod 2 is the Rokhlin invariant.… See more
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- 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.
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 …
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
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 …
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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 …
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.
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 …
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 …
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 …
[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 …
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 …
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 …
RATIONAL HOMOLOGY 3-SPHERES AND SL(2;C) REPRESENTATIONS SUDIPTA GHOSH, STEVEN SIVEK, AND RAPHAEL ZENTNER Abstract. We use instanton gauge theory to …
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 …
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} …
3-MANIFOLDS, KNOTS, AND HOMOLOGY 3-SPHERES
In studying homology spheres, we were able to look at two related invariants, that of Casson and of Rokhlin, which we have seen have many applications to our understanding the topology of …
Why are invariants of Homology 3-Spheres interesting?
Jan 4, 2014 · Even with the Poincare conjecture solved, invariants of homology 3 3 -spheres are a good first step in the classification of all smooth 3 3 -manifolds - a classification which is …
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 …
Rapid traversal of vast chemical space using machine learning …
5 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 …
