Topological groupoids: I. universal constructions

1976 ◽  
Vol 71 (1) ◽  
pp. 273-286 ◽  
Author(s):  
Ronald Brown ◽  
J. P. L. Hardy
Keyword(s):  
Universal Constructions ◽  
Topological Groupoids

scholarly journals Rigid cohomology of topological groupoids

1978 ◽  
Vol 26 (3) ◽  
pp. 277-301 ◽  
Author(s):  
K. A. MacKenzie
Keyword(s):  
Vector Bundles ◽  
Cohomology Theory ◽  
Unexpected Result ◽  
Vertex Group ◽  
Topological Groups ◽  
Locally Compact ◽  
Cohomology Space ◽  
Rigid Cohomology ◽  
Topological Groupoids

AbstractA cohomology theory for locally trivial, locally compact topological groupoids with coefficients in vector bundles is constructed, generalizing constructions of Hochschild and Mostow (1962) for topological groups and Higgins (1971) for discrete groupoids. It is calculated to be naturally isomorphic to the cohomology of the vertex groups, and is thus independent of the twistedness of the groupoid. The second cohomology space is accordingly realized as those “rigid” extensions which essentially arise from extensions of the vertex group; the cohomological machinery now yields the unexpected result that in fact all extensions, satisfying some natural weak conditions, are rigid.

scholarly journals Restricted Algebras on Inverse Semigroups—Part II: Positive Definite Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Massoud Amini ◽  
Alireza Medghalchi
Keyword(s):  
Inverse Semigroup ◽  
Harmonic Analysis ◽  
Positive Definite ◽  
Inverse Semigroups ◽  
Positive Definite Functions ◽  
Topological Groups ◽  
Topological Groupoids

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. In this paper, we investigate the concept of restricted positive definite functions and their relation with restricted representations of an inverse semigroup. We also introduce the restricted Fourier and Fourier-Stieltjes algebras of an inverse semigroup and study their relation with the corresponding algebras on the associated groupoid.

scholarly journals Extendibility, monodromy, and local triviality for topological groupoids

2001 ◽  
Vol 27 (3) ◽  
pp. 131-140 ◽  
Author(s):  
Osman Mucuk ◽  
İlhan İçen
Keyword(s):  
Universal Cover ◽  
Small Category ◽  
Topological Groupoid ◽  
Fundamental Groupoid ◽  
Topological Groupoids

A groupoid is a small category in which each morphism has an inverse. A topological groupoid is a groupoid in which both sets of objects and morphisms have topologies such that all maps of groupoid structure are continuous. The notion of monodromy groupoid of a topological groupoid generalizes those of fundamental groupoid and universal cover. It was earlier proved that the monodromy groupoid of a locally sectionable topological groupoid has the structure of a topological groupoid satisfying some properties. In this paper a similar problem is studied for compatible locally trivial topological groupoids.

scholarly journals Universal minimal flow in the theory of topological groupoids

2020 ◽  
Vol 14 (2) ◽  
pp. 513-537
Author(s):  
Riccardo Re ◽  
Pietro Ursino
Keyword(s):  
Minimal Flow ◽  
Topological Groupoids

THE EXQUISITE GEOMETRIC STRUCTURE OF A CENTRAL LIMIT THEOREM

Fractals ◽  
2003 ◽  
Vol 11 (01) ◽  
pp. 39-52 ◽  
Author(s):  
CARLOS E. PUENTE
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Geometric Structure ◽  
Limit Theorems ◽  
Probability Distributions ◽  
Space Filling ◽  
Gaussian Distributions ◽  
Bivariate Gaussian Distribution ◽  
Universal Constructions

Universal constructions of univariate and bivariate Gaussian distributions, as transformations of diffuse probability distributions via, respectively, plane- and space-filling fractal interpolating functions and the central limit theorems that they imply, are reviewed. It is illustrated that the construction of the bivariate Gaussian distribution yields exotic kaleidoscopic decompositions of the bell in terms of exquisite geometric structures which include non-trivial crystalline patterns having arbitrary n-fold symmetry, for any n > 2. It is shown that these results also hold when fractal interpolating functions are replaced by a more general class of attractors that are not functions.

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