The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
S. K. Geetha - One of the best experts on this subject based on the ideXlab platform.
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F-semigroup Compactifications
Fuzzy Sets and Systems, 1992Co-Authors: S. K. GeethaAbstract:Abstract In this paper we discuss Compactifications of a fuzzy topological semigroup. We prove that corresponding to the Bohr compactification of a topological semigroup, the Bohr fuzzy compactification exists for a topologically generated fuzzy topological semigroup. We also introduce F-semigroup compactification analogous to the notion of semigroup Compactifications of topological semigroups, and prove that the set of all F-semigroup Compactifications of a fuzzy topological semigroup is an upper complete semilattice.
Pekka Salmi - One of the best experts on this subject based on the ideXlab platform.
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quantum semigroup Compactifications and uniform continuity on locally compact quantum groups
Illinois Journal of Mathematics, 2010Co-Authors: Pekka SalmiAbstract:We introduce quantum semigroup Compactifications and study the universal quantum semigroup compactification of a coamenable locally compact quantum group. If G is a classical locally compact group, the universal semigroup compactification corresponds to the C*-algebra of the bounded left uniformly continuous functions on G, so we study the analogous C*-algebra associated with a locally compact quantum group.
Romyar T Sharifi - One of the best experts on this subject based on the ideXlab platform.
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Compactifications of s arithmetic quotients for the projective general linear group
arXiv: Number Theory, 2015Co-Authors: Takako Fukaya, Kazuya Kato, Romyar T SharifiAbstract:Let F be a global field, and let S be a finite set of places of F containing all archimedean places. Consider the product X of the symmetric spaces and Bruhat-Tits buildings for PGL_d of the completions of F at archimedean and non-archimedean places in S, respectively. We construct Compactifications of the quotient of X by S-arithmetic subgroups of PGL_d(F). The constructions make delicate use of reductive Borel-Serre spaces for archimedean places and polyhedral and seminorm Compactifications at nonarchimedean places. We also briefly discuss a few potential applications of our compacifications.
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Compactifications of s arithmetic quotients for the projective general linear group
Conference on Elliptic Curves Modular Forms and Iwasawa Theory held in honour of the 70th birthday of John H. Coates 2015, 2015Co-Authors: Takako Fukaya, Kazuya Kato, Romyar T SharifiAbstract:Let F be a global field, let S be a nonempty finite set of places of F which contains the archimedean places of F, let \(d\geqslant 1\), and let \(X =\prod _{v\in S} X_v\) where \(X_v\) is the symmetric space (resp., Bruhat-Tits building) associated to \({{\mathrm{PGL}}}_d(F_v)\) if v is archimedean (resp., non-archimedean). In this paper, we construct Compactifications \(\Gamma \backslash \bar{X}\) of the quotient spaces \(\Gamma \backslash X\) for S-arithmetic subgroups \(\Gamma \) of \({{\mathrm{PGL}}}_d(F)\). The constructions make delicate use of the maximal Satake compactification of \(X_v\) (resp., the polyhedral compactification of \(X_v\) of Gerardin and Landvogt) for v archimedean (resp., non-archimedean). We also consider a variant of \(\bar{X}\) in which we use the standard Satake compactification of \(X_v\) (resp., the compactification of \(X_v\) due to Werner).
Armand Borel - One of the best experts on this subject based on the ideXlab platform.
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Compactifications of Symmetric and Locally Symmetric Spaces
2005Co-Authors: Armand BorelAbstract:* Preface * Introduction Part I: Compactifications of Riemannian Symmetric Spaces * Review of Classical Compactifications of Symmetric Spaces * Uniform Construction of Compactifications of Symmetric Spaces * Properties of Compactifications of Symmetric Spaces Part II: Smooth Compactifications of Semisimple Symmetric Spaces * Smooth Compactifications of Riemannian Symmetric Spaces G / K * Semisimple Symmetric Spaces G / H * The Real Points of Complex Symmetric Spaces Defined Over R * The DeConcini-Procesi Compactification of a Complex Symmetric Space and its Real Points * The Oshima-Sekiguchi Compactification of G / K and Comparison with G/Hw (R) Part III: Compactifications of Locally Symmetric Spaces * Classical Compactifications of Locally Symmetric Spaces * Uniform Construction of Compactifications of Locally Symmetric Spaces * Properties of Compactifications of Locally Symmetric Spaces * Subgroup Compactifications of o \ G * Metric Properties of Compactifications of Locally Symmetric Spaces o \ X * References * Index
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Compactifications of Symmetric Spaces
1996Co-Authors: Armand BorelAbstract:Compactifications of symmetric spaces have been constructed by different methods for various applications. One application is to provide the so-called rational boundary components which can be used to compactify locally symmetric spaces. In this paper, we construct many Compactifications of symmetric spaces using a uniform method, which is motivated by the Borel-Serre compactification of locally symmetric spaces. Besides unifying Compactifications of both symmetric and locally symmetric spaces, this uniform construction allows one to compare and relate easily different Compactifications, to extend the group action continuously to boundaries of Compactifications, and to clarify the structure of the boundaries.
Richard Wentworth - One of the best experts on this subject based on the ideXlab platform.
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complex algebraic Compactifications of the moduli space of hermitian yang mills connections on a projective manifold
arXiv: Differential Geometry, 2018Co-Authors: Daniel Greb, Benjamin Sibley, Matei Toma, Richard WentworthAbstract:In this paper we study the relationship between three Compactifications of the moduli space of Hermitian-Yang-Mills connections on a fixed Hermitian vector bundle over a projective algebraic manifold of arbitrary dimension. Via the Donaldson-Uhlenbeck-Yau theorem, this space is analytically isomorphic to the moduli space of stable holomorphic vector bundles, and as such it admits an algebraic compactification by Gieseker-Maruyama semistable torsion-free sheaves. A recent construction due to the first and third authors gives another compactification as a moduli space of slope semistable sheaves. In the present article, following fundamental work of Tian generalising the analysis of Uhlenbeck and Donaldson in complex dimension two, we define a gauge theoretic compactification by adding certain ideal connections at the boundary. Extending work of Jun Li in the case of bundles on algebraic surfaces, we exhibit comparison maps from the sheaf theoretic Compactifications and prove their continuity. The continuity, together with a delicate analysis of the fibres of the map from the moduli space of slope semistable sheaves allows us to endow the gauge theoretic compactification with the structure of a complex analytic space.
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Gromov Invariants for Holomorphic Maps from Riemann Surfaces to Grassmannians
arXiv: Algebraic Geometry, 1993Co-Authors: Aaron Bertram, Georgios Daskalopoulos, Richard WentworthAbstract:Two Compactifications of the space of holomorphic maps of fixed degree from a compact Riemann surface to a Grassmannian are studied. It is shown that the Uhlenbeck compactification has the structure of a projective scheme and is dominated by the algebraic compactification arising as a Grothendieck Quot scheme. The latter may be embedded into the moduli space of solutions to a generalized version of the vortex equations studied by Bradlow. This gives an effective way of computing certain intersection numbers (known as Gromov invariants) on the space of holomorphic maps into Grassmannians. We carry out these computations in the case where the Riemann surface has genus one.