Constructing a Fake 4-manifold by Gluck Construction to a Standard 4-manifold
نویسندگان
چکیده
LET S3 G S’ denote the twisted S3 bundle over S’. In this paper we will demonstrate an imbedding of a 2-sphere f:S* 4 S3 G S’ #S* x S* such that twisting S3 g S’ #S’ x S* along f(S*) (Gluck construction) produces a fake manifold M4. In fact M4 coincides with the fake S3 2 S’ #S* x S*‘s of [l] and 123. More specifically, if IV;= M-int(B3 g S’) (a fake B3 z S’ # S* x S*) and Q4 is the Cappell-Shaneson’s fake RP4 corresponding to the matrix,
منابع مشابه
Scharlemann’s manifold is standard
In his 1974 thesis, Martin Scharlemann constructed a fake homotopy equivalence from a closed smooth manifold f : Q → S3 × S1#S2 × S2, and asked the question whether or not the manifold Q itself is diffeomorphic to S3 × S1#S2 × S2. Here we answer this question affirmatively. In [Sc] Scharlemann showed that if Σ3 is the Poincaré homology 3-sphere, by surgering the 4-manifold Σ× S, along a loop in...
متن کاملآموزش منیفلد با استفاده از تشکیل گراف منیفلدِ مبتنی بر بازنمایی تنک
In this paper, a sparse representation based manifold learning method is proposed. The construction of the graph manifold in high dimensional space is the most important step of the manifold learning methods that is divided into local and gobal groups. The proposed graph manifold extracts local and global features, simultanstly. After construction the sparse representation based graph manifold,...
متن کاملVolume-minimizing Foliations on Spheres
The volume of a k-dimensional foliation F in a Riemannian manifold Mn is defined as the mass of image of the Gauss map, which is a map from M to the Grassmann bundle of k-planes in the tangent bundle. Generalizing the construction by Gluck and Ziller in [4], “singular” foliations by 3-spheres are constructed on round spheres S, as well as a singular foliation by 7-spheres on S, which minimize v...
متن کاملبهبود مدل تفکیککننده منیفلدهای غیرخطی بهمنظور بازشناسی چهره با یک تصویر از هر فرد
Manifold learning is a dimension reduction method for extracting nonlinear structures of high-dimensional data. Many methods have been introduced for this purpose. Most of these methods usually extract a global manifold for data. However, in many real-world problems, there is not only one global manifold, but also additional information about the objects is shared by a large number of manifolds...
متن کاملof the Manifold Atlas ( 2013 ) Fake lens spaces *
A fake lens space is an orbit space of a free action of a finite cyclic group on a sphere and as such it is a generalization of a classical lens space. The invariants of fake lens spaces described here are their homotopy groups, homology groups, a certain k-invariant, the Reidemeister torsion, the ρ-invariant and certain splitting invariants. We survey the classification of fake lens spaces whi...
متن کامل