scholarly journals Isometric embedding of a smooth compact manifold with a metric of low regularity

1978 ◽  
Vol 16 (1-2) ◽  
pp. 29-50 ◽  
Author(s):  
Anders Källén
Keyword(s):  
Compact Manifold ◽  
Isometric Embedding ◽  
Low Regularity ◽  
Smooth Compact Manifold

scholarly journals CONFIGURATION CATEGORIES AND HOMOTOPY AUTOMORPHISMS

2018 ◽  
Vol 62 (1) ◽  
pp. 13-41
Author(s):  
MICHAEL S. WEISS
Keyword(s):  
Compact Manifold ◽  
Geometric Conditions ◽  
Homeomorphism Group ◽  
Manifold With Boundary ◽  
Smooth Compact Manifold

AbstractLet M be a smooth compact manifold with boundary. Under some geometric conditions on M, a homotopical model for the pair (M, ∂M) can be recovered from the configuration category of M \ ∂M. The grouplike monoid of derived homotopy automorphisms of the configuration category of M \ ∂M then acts on the homotopical model of (M, ∂M). That action is compatible with a better known homotopical action of the homeomorphism group of M \ ∂M on (M, ∂M).

scholarly journals Homology stability for symmetric diffeomorphism and mapping class groups

2015 ◽  
Vol 160 (1) ◽  
pp. 121-139 ◽  
Author(s):  
ULRIKE TILLMANN
Keyword(s):  
Compact Manifold ◽  
Smooth Manifold ◽  
Mapping Class Groups ◽  
Mapping Class ◽  
Classifying Spaces ◽  
Class Groups ◽  
Connected Sum ◽  
Smooth Compact Manifold ◽  
Embedded Disks ◽  
Homology Stability

AbstractFor any smooth compact manifold W with boundary of dimension of at least two we prove that the classifying spaces of its group of diffeomorphisms which fix a set of k points or k embedded disks (up to permutation) satisfy homology stability. The same is true for so-called symmetric diffeomorphisms of W connected sum with k copies of an arbitrary compact smooth manifold Q of the same dimension. The analogues for mapping class groups as well as other generalisations will also be proved.

scholarly journals Bistable vector fields are axiom A

1995 ◽  
Vol 51 (1) ◽  
pp. 83-86
Author(s):  
Mike Hurley
Keyword(s):  
Vector Field ◽  
Compact Manifold ◽  
Vector Fields ◽  
Axiom A ◽  
Smooth Compact Manifold ◽  
Structurally Stable

Recently L. Wen showed that if a C1 vector field (on a smooth compact manifold without boundary) is both structurally stable and topologically stable then it will satisfy Axiom A. The purpose of this note is to indicate how results from an earlier paper can be used to simplify somewhat Wen's argument.

Some embeddings of projective spaces

1959 ◽  
Vol 55 (4) ◽  
pp. 294-298 ◽  
Author(s):  
I. M. James
Keyword(s):  
Euclidean Space ◽  
Compact Manifold ◽  
Projective Spaces ◽  
Dimensional Euclidean Space ◽  
Smooth Compact Manifold

1. Introduction. We say that a smooth compact manifold is embedded in q–space when there is given a regular one-one map of the manifold into q–dimensional Euclidean space. Whitney (5) has shown that embeddings always exist when q is not less than twice the dimension of the manifold.

scholarly journals Duality by reproducing kernels

2003 ◽  
Vol 2003 (6) ◽  
pp. 327-395 ◽  
Author(s):  
A. Shlapunov ◽  
N. Tarkhanov
Keyword(s):  
Differential Operator ◽  
Neumann Problem ◽  
Compact Manifold ◽  
Reproducing Kernels ◽  
Elliptic Differential Operator ◽  
Regularity Theorem ◽  
Neumann Problems ◽  
Smooth Compact Manifold ◽  
Convexity Properties ◽  
The Neumann Problem

LetAbe a determined or overdetermined elliptic differential operator on a smooth compact manifoldX. Write𝒮A(𝒟)for the space of solutions of the systemAu=0in a domain𝒟⋐X. Using reproducing kernels related to various Hilbert structures on subspaces of𝒮A(𝒟), we show explicit identifications of the dual spaces. To prove the regularity of reproducing kernels up to the boundary of𝒟, we specify them as resolution operators of abstract Neumann problems. The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the∂¯-Neumann problem. The duality itself takes place only for those domains𝒟which possess certain convexity properties with respect toA.

scholarly journals Diffeomorphisms on the fuzzy sphere

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Goro Ishiki ◽  
Takaki Matsumoto
Keyword(s):  
Configuration Space ◽  
Compact Manifold ◽  
Finite Size ◽  
Fuzzy Sphere ◽  
Algebra Of Functions ◽  
Large N ◽  
Smooth Compact Manifold ◽  
The Matrix ◽  
Area Preserving ◽  
Matrix Regularization

Abstract Diffeomorphisms can be seen as automorphisms of the algebra of functions. In matrix regularization, functions on a smooth compact manifold are mapped to finite-size matrices. We consider how diffeomorphisms act on the configuration space of the matrices through matrix regularization. For the case of the fuzzy $$S^2$, we construct the matrix regularization in terms of the Berezin–Toeplitz quantization. By using this quantization map, we define diffeomorphisms on the space of matrices. We explicitly construct the matrix version of holomorphic diffeomorphisms on $$S^2$. We also propose three methods of constructing approximate invariants on the fuzzy $$S^2$. These invariants are exactly invariant under area-preserving diffeomorphisms and only approximately invariant (i.e. invariant in the large-$$N$ limit) under general diffeomorphisms.

scholarly journals Riemannian foliations with parallel curvature

1983 ◽  
Vol 90 ◽  
pp. 145-153
Author(s):  
Robert A. Blumenthal
Keyword(s):  
Tangent Bundle ◽  
Normal Bundle ◽  
Compact Manifold ◽  
Riemannian Metric ◽  
Riemannian Foliation ◽  
Riemannian Foliations ◽  
Smooth Compact Manifold

Let M be a smooth compact manifold and let be a smooth codimension q Riemannian foliation of M. Let T(M) be the tangent bundle of M and let E ⊂ T(M) be the subbundle tangent to . We may regard the normal bundle Q = T(M)/E of as a subbundle of T(M) satisfying T(M) = E ⊕ Q. Let g be a smooth Riemannian metric on Q invariant under the natural parallelism along the leaves of .

scholarly journals An Intrinsic Characterization of Five Points in a CAT(0) Space

2020 ◽  
Vol 8 (1) ◽  
pp. 114-165
Author(s):  
Tetsu Toyoda
Keyword(s):  
Metric Space ◽  
Isometric Embedding ◽  
Metric Spaces ◽  
Necessary Conditions ◽  
New Approach ◽  
Intrinsic Characterization ◽  
New Family

AbstractGromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov. In this paper, we prove that a metric space X containing at most five points admits an isometric embedding into a CAT(0) space if and only if any four points in X satisfy the ⊠-inequalities. To prove this, we introduce a new family of necessary conditions for a metric space to admit an isometric embedding into a CAT(0) space by modifying and generalizing Gromov’s cycle conditions. Furthermore, we prove that if a metric space satisfies all those necessary conditions, then it admits an isometric embedding into a CAT(0) space. This work presents a new approach to characterizing those metric spaces that admit an isometric embedding into a CAT(0) space.

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