Rigidities of asymptotically Euclidean manifolds

1999 ◽  
Vol 60 (3) ◽  
pp. 521-528 ◽  
Author(s):  
Seong-Hun Paeng
Keyword(s):  
Riemannian Manifold ◽  
Euclidean Space ◽  
Fundamental Group ◽  
Compact Riemannian Manifold ◽  
Universal Covering ◽  
Covering Space ◽  
Universal Covering Space

Let M be an n-dimensional compact Riemannian manifold. We study the fundamental group of M when the universal covering space of M, M is close to some Euclidean space ℝs asymptotically.

Spherical Mean and the Fundamental Group

1991 ◽  
Vol 34 (1) ◽  
pp. 3-11 ◽  
Author(s):  
Toshiaki Adachi
Keyword(s):  
Riemannian Manifold ◽  
Fundamental Group ◽  
Random Walks ◽  
Isoperimetric Inequality ◽  
Lower Bounds ◽  
Compact Riemannian Manifold ◽  
Universal Covering ◽  
Spherical Means ◽  
Universal Covering Space ◽  
Spherical Mean

AbstractWe investigate some properties of spherical means on the universal covering space of a compact Riemannian manifold. If the fundamental group is amenable then the greatest lower bounds of the spectrum of spherical Laplacians are equal to zero. If the fundamental group is nontransient so are geodesic random walks. We also give an isoperimetric inequality for spherical means.

On Wh3 of a Bieberbach group

1984 ◽  
Vol 95 (1) ◽  
pp. 55-60
Author(s):  
Andrew J. Nicas
Keyword(s):  
Fundamental Group ◽  
Universal Covering ◽  
Closed Manifold ◽  
Covering Space ◽  
Whitehead Group ◽  
Bieberbach Group ◽  
Universal Covering Space ◽  
Aspherical Manifold

A closed aspherical manifold is a closed manifold whose universal covering space is contractible. There is the following conjecture concerning the algebraic K-theory of such manifolds:Conjecture. Let Γ be the fundamental group of a closed aspherical manifold. Then Whi(Γ) = 0 for i ≥ 0 where Whi(Γ) is the i-th higher Whitehead group of Γ.

An infinite family of non-Haken hyperbolic 3-manifolds with vanishing Whitehead groups

1986 ◽  
Vol 99 (2) ◽  
pp. 239-246 ◽  
Author(s):  
Andrew J. Nicas
Keyword(s):  
Fundamental Group ◽  
Infinite Family ◽  
Universal Covering ◽  
Covering Space ◽  
Homotopy Equivalence ◽  
Universal Covering Space ◽  
Aspherical Manifold ◽  
Aspherical Manifolds ◽  
Whitehead Groups

A manifold M is said to be aspherical if its universal covering space is contractible. Farrell and Hsiang have conjectured [3]:Conjecture A. (Topological rigidity of aspherical manifolds.) Any homotopy equivalence f: N → M between closed aspherical manifolds is homotopic to a homeomorphism,and its analogue in algebraic K-theory:Conjecture B. The Whitehead groups Whj(π1M)(j ≥ 0) of the fundamental group of a closed aspherical manifold M vanish.

scholarly journals On 4-manifolds with universal covering space a compact geometric manifold

1993 ◽  
Vol 55 (2) ◽  
pp. 137-148
Author(s):  
Jonathan A. Hillman
Keyword(s):  
Fundamental Group ◽  
Euler Characteristic ◽  
Homotopy Type ◽  
Universal Covering ◽  
Total Space ◽  
Covering Space ◽  
Compact Type ◽  
Universal Covering Space

AbstractThere are 11 closed 4-manifolds which admit geometries of compact type (S4, CP2 or S2 × S2) and two other closely related bundle spaces (S2 × S2 and the total space of the nontrivial RP2-bundle over S2). We show that the homotopy type of such a manifold is determined up to an ambiguity of order at most 4 by its quadratic 2-type, and this in turn is (in most cases) determined by the Euler characteristic, fundamental group and Stiefel-Whitney classes. In (at least) seven of the 13 cases, a PL 4-manifold with the same invariants as a geometric manifold or bundle space must be homeomorphic to it.

A Note on the Universal Covering Space of a Surface

1971 ◽  
Vol 78 (5) ◽  
pp. 505 ◽  
Author(s):  
G. W. Knutson
Keyword(s):  
Universal Covering ◽  
Covering Space ◽  
Universal Covering Space

A quadratic parabolic group

1975 ◽  
Vol 77 (2) ◽  
pp. 281-288 ◽  
Author(s):  
Robert Riley
Keyword(s):  
Normal Form ◽  
Half Space ◽  
Transformation Group ◽  
Universal Covering ◽  
Covering Space ◽  
Fundamental Domains ◽  
Universal Covering Space ◽  
Other Information ◽  
Figure Eight Knot

When k is a 2-bridge knot with group πK, there are parabolic representations (p-reps) θ: πK → PSL(): = PSL(2, ). The most obvious problem that this suggests is the determination of a presentation for an image group πKθ. We shall settle the easiest outstanding case in section 2 below, viz. k the figure-eight knot 41, which has the 2-bridge normal form (5, 3). We shall prove that the (two equivalent) p-reps θ for this knot are isomorphisms of πK on πKθ. Furthermore, the universal covering space of S3\k can be realized as Poincaré's upper half space 3, and πKθ is a group of hyperbolic isometries of 3 which is also the deck transformation group of the covering 3 → S3\k. The group πKθ is a subgroup of two closely related groups that we study in section 3. We shall give fundamental domains, presentations, and other information for all these groups.

scholarly journals Centroidal Voronoi tessellation in universal covering space of manifold surfaces

2011 ◽  
Vol 28 (8) ◽  
pp. 475-496 ◽  
Author(s):  
Guodong Rong ◽  
Miao Jin ◽  
Liang Shuai ◽  
Xiaohu Guo
Keyword(s):  
Voronoi Tessellation ◽  
Universal Covering ◽  
Covering Space ◽  
Universal Covering Space ◽  
Centroidal Voronoi Tessellation

scholarly journals A presentation for a group of automorphisms of a simplicial complex

1988 ◽  
Vol 30 (3) ◽  
pp. 331-337 ◽  
Author(s):  
M. A. Armstrong
Keyword(s):  
Simplicial Complex ◽  
Elementary Proof ◽  
Universal Covering ◽  
Covering Space ◽  
Covering Spaces ◽  
Group Of Automorphisms ◽  
Generators And Relations ◽  
Universal Covering Space ◽  
Simply Connected ◽  
Special Case

The Bass–Serre theorem supplies generators and relations for a group of automorphisms of a tree. Recently K. S. Brown [2] has extended the result to produce a presentation for a group of automorphisms of a simply connected complex, the extra ingredient being relations which come from the 2-cells of the complex. Suppose G is the group, K the complex and L the 1-skeleton of K. Then an extension of π1(L) by G acts on the universal covering space of L (which is of course a tree) and Brown's technique is to apply the work of Bass and Serre to this action. Our aim is to give a direct elementary proof of Brown's theorem which makes no use of covering spaces, deals with the Bass–Serre theorem as a special case and clarifies the roles played by the various generators and relations.

scholarly journals Resilient Routing for Sensor Networks Using Hyperbolic Embedding of Universal Covering Space

2010 ◽  
Author(s):  
Wei Zeng ◽  
Rik Sarkar ◽  
Feng Luo ◽  
Xianfeng Gu ◽  
Jie Gao
Keyword(s):  
Sensor Networks ◽  
Universal Covering ◽  
Covering Space ◽  
Universal Covering Space ◽  
Hyperbolic Embedding
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