KLEINIAN GROUPS WITH REAL PARAMETERS

2001 ◽  
Vol 03 (02) ◽  
pp. 163-186 ◽  
Author(s):  
F. W. GEHRING ◽  
J. P. GILMAN ◽  
G. J. MARTIN
Keyword(s):  
General Structure ◽  
Kleinian Groups ◽  
Analytic Space ◽  
Fuchsian Groups ◽  
Discrete Groups ◽  
Möbius Groups

We find all real points of the analytic space of two generator Möbius groups with one generator elliptic of order two. Geometrically this is a certain slice through the space of two generator discrete groups, analogous to the Riley slice, though of a very different nature. We obtain applications concerning the general structure of the space of all two generator Kleinian groups and various universal constraints for Fuchsian groups.

Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups

1987 ◽  
Vol 102 (2) ◽  
pp. 251-257 ◽  
Author(s):  
C. MacLachlan ◽  
A. W. Reid
Keyword(s):  
Kleinian Groups ◽  
Fuchsian Groups ◽  
Arithmetic Groups ◽  
Quaternion Algebras ◽  
Isomorphism Classes ◽  
Similar Characterization ◽  
One To One

Arithmetic Fuchsian and Kleinian groups can all be obtained from quaternion algebras (see [2,12]). In a series of papers ([8,9,10,11]), Takeuchi investigated and characterized arithmetic Fuchsian groups among all Fuchsian groups of finite covolume, in terms of the traces of the elements in the group. His methods are readily adaptable to Kleinian groups, and we obtain a similar characterization of arithmetic Kleinian groups in §3. Commensurability classes of Kleinian groups of finite co-volume are discussed in [2] and it is shown there that the arithmetic groups can be characterized as those having dense commensurability subgroup. Here the wide commensurability classes of arithmetic Kleinian groups are shown to be approximately in one-to-one correspondence with the isomorphism classes of the corresponding quaternion algebras (Theorem 2) and it easily follows that there are infinitely many wide commensurability classes of cocompact Kleinian groups, and hence of compact hyperbolic 3-manifolds.

scholarly journals On Teichmüller Spaces of Koebe Groups

1997 ◽  
Vol 08 (05) ◽  
pp. 611-632
Author(s):  
Pablo Arés Gastesi
Keyword(s):  
Teichmüller Space ◽  
Universal Covering ◽  
Kleinian Groups ◽  
Fuchsian Groups ◽  
Teichmuller Space ◽  
Isomorphism Theorem ◽  
Teichmüller Spaces ◽  
Teichmuller Spaces ◽  
Covering Group

In this paper we study the Teichmüller space of constructible Koebe groups. These are Kleinian groups arising from planar covering of 2-orbifolds. In the first part, we parametrize the Teichmüller spaces of Koebe groups using a technique that can be applied to explicitly compute generators of these groups, maybe by programming a computer. In the second part, we study some properties of these Teichmüller spaces. More precisely, we find the covering group of these spaces (the universal covering is the Teichmüller space of the punctured surface), and prove an isomorphism theorem similar to the Bers–Greenberg theorem for Fuchsian groups.

The Classification of Non-Euclidean Plane Crystallographic Groups

1967 ◽  
Vol 19 ◽  
pp. 1192-1205 ◽  
Author(s):  
A. M. Macbeath
Keyword(s):  
Hyperbolic Plane ◽  
Euclidean Plane ◽  
Quotient Space ◽  
Fuchsian Groups ◽  
Discrete Groups ◽  
Crystallographic Groups ◽  
Algebraic Classification ◽  
Compact Quotient

This paper deals with the algebraic classification of non-euclidean plane crystallographic groups (NEC groups, for short) with compact quotient space. The groups considered are the discrete groups of motions of the Lobatschewsky or hyperbolic plane, including those which contain orientation-reversing reflections and glide-reflections. The corresponding problem for Fuchsian groups, which contain only orientable transformations, is essentially solved in the work of Fricke and Klein (6).

scholarly journals Chebyshev polynomials and inequalities for Kleinian groups

2021 ◽  
Author(s):  
Hala Alaqad ◽  
Jianhua Gong ◽  
Gaven Martin
Keyword(s):  
Chebyshev Polynomials ◽  
Kleinian Groups ◽  
Necessary Condition ◽  
Complex Numbers ◽  
Discrete Groups ◽  
Low Dimensional Topology ◽  
Principal Character ◽  
Group A ◽  
Low Dimensional ◽  
Jørgensen’S Inequality

The principal character of a representation of the free group of rank two into [Formula: see text] is a triple of complex numbers that determines an irreducible representation uniquely up to conjugacy. It is a central problem in the geometry of discrete groups and low dimensional topology to determine when such a triple represents a discrete group which is not virtually abelian, that is, a Kleinian group. A classical necessary condition is Jørgensen’s inequality. Here, we use certain shifted Chebyshev polynomials and trace identities to determine new families of such inequalities, some of which are best possible. The use of these polynomials also shows how we can identify the principal character of some important subgroups from that of the group itself.

Cloning of the Rat Tissue Factor cDNA and Promoter: Identification of a Serum-response Region

1996 ◽  
Vol 76 (05) ◽  
pp. 697-702 ◽  
Author(s):  
Olivier Taby ◽  
Claire-Lise Rosenfield ◽  
Vladimir Bogdanov ◽  
Yale Nemerson ◽  
Mark B Taubman
Keyword(s):  
Tissue Factor ◽  
General Structure ◽  
Amino Acid Sequences ◽  
Proximal Promoter ◽  
Striking Similarity ◽  
Upstream Sequence ◽  
Tf Gene ◽  
Rat Tissue ◽  
High Degree ◽  
Transcriptional Elements

SummaryTissue factor (TF) initiates coagulation and its expression in vascular smooth muscle cells (VSMC) likely plays a role in the propagation of arterial thrombosis. We report cloning the cDNA and proximal promoter region of the rat TF gene. While maintaining the general structure and organization of the TF molecule, there is a surprising divergence (≈ 18%) between the derived amino acid sequences of the rat and mouse TF. In contrast, there is striking similarity (90%) in the 5’ untranslated regions. High levels of basal promoter activity were seen in rat VSMC with constructs containing 106 bp of sequence downstream from the putative transcription start site and 426 to 103 bp of upstream sequence. Deletion of the sequence from −103 to −79, containing a single SP1 site, removed virtually all of the basal and serum-induced activity. Removal of the NFkB site or two additional upstream SP1 sites had little effect on serum responsiveness. Removal of the 5’ untranslated region abolished most of the basal activity of the TF promoter, suggesting that its high degree of conservation may be due to the presence of transcriptional elements critical for TF expression in rodent VSMC.

"GENERAL STRUCTURE AND REQUIREMENTS FOR THE GEOKHOD CONTROL SYSTEM "

2017 ◽  
Vol 17 (6) ◽  
pp. 41-46
Author(s):  
V.V. Aksenov ◽  
◽  
I.V. Chicherin ◽  
Keyword(s):  
Control System ◽  
General Structure
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