نتایج جستجو برای: Covering space

تعداد نتایج: 541872  

Journal: :J. London Math. Society 2011
Alessandro Berarducci Marcello Mamino

We consider definably compact groups in an o-minimal expansion of a real closed field. It is known that to each such group G is associated a natural exact sequence 1→ G00 → G → G/G00 → 1 where G00 is the “infinitesimal subgroup” of G and G/G00 is a compact real Lie group. We show that given a connected open subset U of G/G00 there is a canonical isomorphism between the fundamental group of U an...

2012
Christian Anderson

Given a vector space V and a non-singular quadratic form Q on V , the orthogonal group O(Q) is the subgroup of GL(V ) that preserves Q. The special orthogonal group SO(Q) is given by O(Q) ∩ SL(V ). If Q is the standard inner product on R then SO(Q) is denoted SO(n). This is a connected, compact Lie group. For n > 2, the group is semi-simple. In the case that n is odd, SO(n) corresponds to the D...

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

Journal: :J. Comb. Theory, Ser. B 2005
Shlomo Hoory

For a finite connected graph let be the spectral radius of its universal cover. We prove that for any graph of average degree and derive from it the following generalization of the Alon Boppana bound. If the average degree of the graph after deleting any radius ball is at least , then its second largest eigenvalue in absolute value is at least for some absolute constant . This result is tight i...

2016
JAMES F. DAVIS

The main theorem states that if K is a finite CW-complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X×Sn for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial, then so is the action on X × Sn. Ünlü and Yalçın recently showed that any fi...

Journal: :Eur. J. Comb. 2003
Hirobumi Mizuno Iwao Sato

Let π1 : K H , π2 : H G and π2π1 : K G be three finite regular coverings of graphs, and let σ be a representation of the covering transformation group of π1. We show that the L-function of G associated to the representation of the covering transformation group of π2π1 induced from σ is equal to that of H associated to σ by means of ordinary voltage assignments. © 2003 Elsevier Science Ltd. All ...

2008
Jürgen Jost

If M is compact Kählerian and ρ is semi-simple, that is that the Zariski closure of the image of ρ in GL(n,C) is semi-simple 1, by means of a result of Donaldson (in the case of Riemann surfaces, [5]) and Corlette (in the higher dimensional case, [4]), there exists a unique harmonic metric u on V, equivalently, a ρ-equivariant harmonic map from the universal covering M̃ of M into Pn := GL(n,C)/U...

2009
SAMUEL BLOOM

In this paper, we define the fundamental group of a topological space and explore its structure, and we proceed to prove Van-Kampen’s Theorem, a powerful result useful for calculating the fundamental groups of spaces which decompose into spaces whose fundamental groups are already known. With these tools, we show that the circle, 2-sphere, torus, and figure-8 space are topologically distinct. W...

1999
M. A. Aguilar

Using fibre bundle theory we construct the universal covering group of U(n), Ũ(n), and show that Ũ(n) is isomorphic to the semidirect product SU(n)©s R. We give a bijection between the set of projective representations of U(n) and the set of equivalence classes of certain unitary representations of SU(n) ©s R. Applying Bargmann’s theorem, we give explicit expressions for the liftings of project...

2009
Ibrahim Assem Juan Carlos Bustamante Patrick Le Meur

In this paper, we study the covering theory of laura algebras. We prove that if a connected laura algebra is standard (that is, has a standard connecting component), then it has Galois coverings associated to the coverings of the connecting component. As a consequence, the first Hochschild cohomology group of a standard laura algebra vanishes if and only if it has no proper Galois coverings.

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