230 research outputs found
From wall spaces to CAT(0) cube complexes
No full textWe explain how to adapt a construction due to M. Sageev in order to construct a proper action of a group on a CAT(0) cube complex starting from a proper action of the group on a wall space
A characterization of hyperbolic spaces
No full textWe show that a geodesic metric space, and in particular the Cayley graph of a finitely generated group, is hyperbolic in the sense of Gromov if and only if intersections of any two metric balls balls is itself "almost" a metric ball. In particular, R-trees are characterized among the class of geodesic metric spaces by the property that the intersection of any two metric balls is always a metric ball. A variation on the definition of "almost" allows us to characterise CAT(k) geometry for k ? 0 in the same way
The first ℓ<sup>2</sup>-Betti number and groups acting on trees
No full textWe generalise results of Thomas, Allcock, Thom-Petersen, and Kar-Niblo to the first ℓ2-Betti number of quotients of certain groups acting on trees by subgroups with free actions on the edge sets of the graphs
New examples of finitely presented groups with strong fixed point properties
No full textWe give an explicit finite presentation of a group normally generated by SL?(?). As a consequence, such a group cannot act on e.g. a finite dimensional contractible manifold or on a compact manifold<br/
On transfer in bounded cohomology
No full text8 pagesWe define a transfer map in the setting of bounded cohomology with certain metric G-module coefficients. As an application, we extend a theorem of Chatterji, Mislin, Pittet and Saloff-Coste on the comparison map from Borel-bounded to Borel cohomology, to cover the case of Lie groups with finitely many connected components
Quo vadis Turkey?
No full text[author of the report: Indira Ceylan]Electronic ed: Istanbul ; Bonn : FES, 2011. - Title only available onlin
Indira Gandhi Canal
No full textThis file contains a digital map of the Indira Gandhi Canal (India) in Google Earth KMZ format that was produced as part of The IBT Water Project at Auburn University. The Indira Gandhi Canal was primarily designed to support irrigation in the Thar Desert region of the state of Rajasthan in western India. Originally called the Rajasthan Canal, the project was renamed in 1984 in honor of the former Prime Minister Indira Gandhi. Stage I of construction began in 1952 and was completed in 1983. This stage is described as consisting of a 204 km feeder canal and 189 km main canal (393 km total). Stage 2 extended the main canal an additional 256 km. Construction appears to be ongoing today as the extent of water distribution expands. As of 2021, the canal appears to feature approximately 200 diversions to secondary distribution canals of varying sizes and approximately 45 control gates to manage flow rates and assist in diverting water to the secondary canals. Metadata embedded in the KMZ file include author contact, Creative Commons License information, and list of references. See the project website (URL shortcut: aub.ie/ibtwater) for information about methods, data sources, additional digital IBT maps, Google Earth tips, and a glossary of key terms
MRS. GANDHI GAVE NEW ECONOMIC APPROACHES
No full textPlenty of food, Sufficient clothing, Proper monitoring of the Key Socio- Economic factors, with commitment to Domestic Productivity were the Essence of the Administrative strategy of Mrs. Indira Gandhi (Late Prime Minister of India). These approaches could be critically related to the remarkable Economic advancement of the Indian sub-continent, with Self- sufficiency in Agriculture, leaving a surplus for export and strides in Industry, Atomic Research, and Space Exploration in India. The author feels that these unique thoughts and approaches of the late Prime Minister could serve as an eye-opener to all the Third World Nations to Accelerate their pace of Social and Economic development. ================================================================ Between 1972 and 1981, the author was a Social worker in India, and a Honorary Consultant for the effective implementation and monitoring of the 20 Point Socio-Economic Development programs designed by Shrimathi Indira Gandhi, the late Prime Minister of India. Centre page article by DR.VSRS in the Barbados Advocate, the largest circulated Daily in Barbados, West Indies, and the English speaking Caribbean Countries. Page 4 - Tuesday - January 8, 1985. During 1982 - 1986, the author was a “Consultant Adviser - Computer Services”, to the Caribbean Development Bank, Barbados, West Indies ( World Bank / UNDP Setup ), under nomination from his assignment as the “Data Processing Expert” to the Commonwealth Fund for Technical Co- operation, London, UK.20 Point Program, Economic Development, Development Ratios, Government Strategy, Indira Gandhi, Key Ratios, Management Decision, Mass Development, Mrs.Gandhi, Political Economics, Productivity, Redefined Productivity, Social Development, Socio-Economic Development
Groups with tame cuts
No full textDans cette thèse, nous étudierons quatre types de suites de fonctions continues à support compact sur un groupe localement compact, à savoir les coupures modérées [caractéristiques] (complètement bornées), et leurs croissances dans l'algèbre de Banach des multiplicateurs de Fourier (complètement bornés). Cette nouvelle notion étend la moyennabilité faible et la propriété de décroissance rapide. L'objectif principal est de fournir des exemples de groupes admettant ou pas ce type de suites, à l'aide d'outils analytiques, algébriques et géométriques.Nous démontrons que les groupes de Baumslag-Solitar BS(p, q) et certains groupes métabéliens de type fini, dont le groupe de l'allumeur de réverbères, admettent des coupures modérées caractéristiques complètement bornées. Ceci est réalisé en montrant que l’existence de coupures modérées [caractéristiques] (complètement bornées) est stables par extension par un groupe à croissance polynomiale. Nous proposerons également une méthode pour construire un groupe de type fini sans coupures modérées en utilisant la propriété (T Schur, G, K).De plus, nous proposerons deux résultats comme applications de coupures modérées. Le premier résultat montre que tout réseau uniforme dans SL(3, R) admet un multiplicateur de Fourier qui n'est pas complètement borné. Ceci fournit un exemple à l'appui de la question ouverte : La moyennabilité d'un groupe discret Γ est-elle caractérisée par le fait que tous les multiplicateurs de Fourier de Γ sont complètement bornés ? Le deuxième résultat est lié à l'application d'induction de McbA(Γ) dans McbA(G) qui est contractante pour tout groupe localement compact G et son réseau Γ. En particulier, lorsque G (ou Γ) est moyennable, l'application d'induction de MA(Γ) dans MA(G) est contractante. Nous démontrerons que la moyennabilité de G est essentielle pour la continuité de cette dernière application.In this thesis, we will study four types of sequences of compactly supported continuous functions on a locally compact group, namely (completely bounded) [characteristic] tame cuts, and their growth in the Banach algebra of (completely bounded) Fourier multipliers. This new notion extends weak amenability and Rapid Decay property. The main goal is to provide examples of groups admitting or not-admittingsuch kind of sequences using analytic, algebraic, and geometric tools.We will prove in particular that the Baumslag-Solitar groups BS(p, q) and some finitely generated metabelian groups, including the Lamplighter group, admit completely bounded characteristic tame cuts. This is achieved by showing that the existence of (completely bounded) [characteristic] tame cuts is stable under extension by a group with polynomial growth. We will also propose a method to construct a finitely generated group without tame cuts using property (T Schur, G, K).In addition, we will propose two results as an application of tame cuts. The first one states that any uniform lattice in SL(3, R) admits a Fourier multiplier that is not completely bounded. This provides a supporting example to the following open question: “Is amenability of a discrete group Γ characterized by the fact that all Fourier multipliers of Γ are completely bounded?” The second application is related to the induction mapping from McbA(Γ) into McbA(G) which is known to be norm decreasing for any locally compact group G and any of its lattice Γ. In particular, when G (or Γ) is amenable, the induction mapping from MA(Γ) into MA(G) is continuous. We will show that the amenability of G is essential for the continuity of the latter mapping
Unitary representations of mapping class groups
No full textLes groupes modulaires de surfaces fermées à points masqués jouent un rôle important comme prototypes par la recherche moderne en théorie géométriques des groupes. La théorie des représentations d'un groupe est un moyen de comprendre à la fois la structure du groupe et ses propriétés dynamiques. Bien qu'il existe beaucoup de littérature sur les représentations unitaires (projectives) de dimension finie des groupes modulaires, il y en a beaucoup moins sur celles de dimension infinie. Le but de cette thèse est d'étudier le groupe modulaire du point de vue des représentations unitaires de dimension infinie, dans le contexte de la théorie géométrique des groupes. Ce mémoire comporte deux parties.Dans la première partie, nous introduisons pour une surface une famille de représentations unitaires de son groupe modulaire, basée sur l'espace des feuillages mesurés. Pour cette famille de représentations, nous montrons qu'aucune d'elles n'a de vecteurs presque invariants. En corollaire, nous obtenons une inégalité concernant l'action du groupe modulaire sur l'espace de Teichmüller. Nous classifions aussi, à équivalence faible près, les représentations unitaires quasi-régulières par rapport à ses sous-groupes géométriques.Dans la seconde partie, pour une surface hyperbolique fermée, nous montrons que la représentation au bord de son groupe modulaire est ergodique, ce qui généralise un résultat classique de Masur sur l'ergodicité de l'action du groupe modulaire sur l'espaces projectif des feuillages mesurés de la surface. En corollaire, nous montrons que la représentation au bord du groupe de modulaire est irréductible, ce qui démontre une conjecture de Bader-Muchnik dans le cas du groupe modulaire par rapport à la classe des mesures de Thurston.Mapping class groups of closed surfaces with punctures play important roles as prototypes of current research in geometric group theory. The representation theory of a group is a way to understand both the group structure and dynamic properties of that group. While there are massive literatures on finite dimensional (projective) unitary representations of mapping class groups, not so much on infinite dimensional ones. The aim of this thesis is to investigate mapping class groups from the perspective of infinite dimensional unitary representations based on current understanding of mapping class groups in the context of geometric group theory. It has two parts. In the first part, for a surface, we introduce a family of unitary representations of its mapping class group based on the space of measured foliations. For this family of representations, we show that none of them has almost invariant vectors. As an application, we obtain an inequality concerning the action of the mapping class group on the Teichmüller space. Moreover, using the same method plus recent results about weak equivalence, we also give a classification, up to weak equivalence, for the unitary quasi-regular representations with respect to geometrical subgroups.In the second part, for a closed hyperbolic surface, we show that the boundary representation of its mapping class group is ergodic, which generalizes the classical result of Masur on ergodicity of the action of the mapping class group on the projective measured foliation space of the surface. As a corollary, we show that the boundary representation of the mapping class group is irreducible. This confirms a conjecture of Bader-Muchnik in the case of mapping class groups with respect to Thurston measure classes
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