A thesis submitted in ful llment of the requirements for the degree of Doctor of Philosophy in Mathematics School of Mathematics University of the Witwatersrand Johannesburg October, 2012 / Let S be an in nite discrete semigroup and S the Stone- Cech compacti cation of S. The operation of S naturally extends to S and makes S a compact right topological semigroup with S contained in the topological center of S. The aim of this thesis is to present the following new results. 1. If S embeddable in a group, then S contains 22jSj pairwise incomparable semiprincipal closed two-sided ideals. 2. Let S be an in nite cancellative semigroup of cardinality and U(S) the set of uniform ultra lters on S. If > !, then there is a closed left ideal decomposition of U(S) such that the corresponding quotient space is homeomorphic to U( ). If = !, then for any connected compact metric space X, there is a closed left ideal decomposition of U(S) with the quotient space homeomorphic to X.

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Thesis (Ph. D.)--Ohio State University, 2009. / Title from first page of PDF file. Includes vita. Includes bibliographical references (p. 220-225).

The set of all compactifications, K(X) of a locally compact, non-compact space X form a complete lattice with βX, the Stone-Čech compactification of X as its largest element, and αX, the one-point compactification of X as its smallest element. For any two locally compact, non-compact spaces X,Y, the lattices K(X), K(Y) are isomorphic if and only if βX - X and βY - Y are homeomorphic. βN is the Stone-Čech compactification of the countable infinite discrete space N. There is an isomorphism between the group of all homeomorphisms of βN and the group of all permutations of N; so βN has c homeomorphisms. The space N* =βN - N has 2c homeomorphisms. The cardinality of the set of orbits of the group of homeomorphisms of N* onto N* is 2c . If f is a homeomorphism of βN into itself, then Pk , the set of all k-periodic points of f is the closure of PkՈN in βN. / Science, Faculty of / Mathematics, Department of / Graduate

We have a look at compactification as a special way of explaining why we only observe 4 spacetime dimensions although theories as string or M-theory require more. In particular, we treat compactification of 11-dimensional supergravity, which is the low energy limit of M-theory, on S4 x T3. At first, we present the basic ideas behind those theories and compactification. Then we introduce important concepts of supersymmetry and supergravity. Afterwards, our particular case of compactification is treated, where we first review the results for the compactification on S4 before we calculate the scalar potential from the reduction ansatz for a so-called twisted torus.

Thesis (Doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1990. / Includes bibliographical references.

Pour une représentation automorphe cuspidale de GL(2,F) avec F un corps de nombres totalement réel, tel que est de type (k, r) et satisfait une condition de pente non critique, l’on construit une distribution p-adique sur le groupe de Galois de l’extension abélienne maximale de F non ramifiée en dehors de p et 1. On démontre que la distribution obtenue est admissible et interpole les valeurs critiques de la fonction L complexe de la représentation automorphe. Cette construction est basée sur l’étude de la cohomologie de la variété modulaire de Hilbert à coefficients surconvergents. / For each cohomological cuspidal automorphic representation for GL(2,F) where F is a totally real number field, such that is of type (k, r) tand satisfies the condition of non critical slope we construct a p-adic distribution on the Galois group of the maximal abelian extension of F unramified outside p and 1. We prove that the distribution is admissible and interpolates the critical values of L-function of the automorphic representation. This construction is based on the study of the overconvergent cohomology of Hilbert modular varieties.

A compact semigroup is, roughly, a semigroup compactification of a locally compact group if it contains a dense homomorphic image of the group. The theory of semigroup compactifications has been developed in connection with subalgebras of continuous bounded functions on locally compact groups. The Eberlein algebra of a locally compact group is defined to be the uniform closure of its Fourier-Stieltjes algebra. In this thesis, we study the semigroup compactification associated with the Eberlein algebra. It is called the Eberlein compactification and it can be constructed as the spectrum of the Eberlein algebra. The algebra of weakly almost periodic functions is one of the most important function spaces in the theory of topological semigroups. Both the weakly almost periodic functions and the associated weakly almost periodic compactification have been extensively studied since the 1930s. The Fourier-Stieltjes algebra, and hence its uniform closure, are subalgebras of the weakly almost periodic functions for any locally compact group. As a consequence, the Eberlein compactification is always a semitopological semigroup and a quotient of the weakly almost periodic compactification. We aim to study the structure and complexity of the Eberlein compactifications. In particular, we prove that for certain Abelian groups, weak^{*}-closed subsemigroups of L^{\infty}[0, 1] may be realized as quotients of their Eberlein compactifications, thus showing that both the Eberlein and weakly almost periodic compactifications are large and complicated in these situations. Moreover, we establish various extension results for the Eberlein algebra and Eberlein compactification and observe that levels of complexity of these structures mimic those of the weakly almost periodic ones. Finally, we investigate the structure of the Eberlein compactification for a certain class of non-Abelian, Heisenberg type locally compact groups and show that aspects of the structure of the Eberlein compactification can be relatively simple.

This thesis gives a functorial interpretation of the Naive Space of Maps Nd as a parametrizing space for a family of maps from certain rational curves to P¹. / text

A compact semigroup is, roughly, a semigroup compactification of a locally compact group if it contains a dense homomorphic image of the group. The theory of semigroup compactifications has been developed in connection with subalgebras of continuous bounded functions on locally compact groups. The Eberlein algebra of a locally compact group is defined to be the uniform closure of its Fourier-Stieltjes algebra. In this thesis, we study the semigroup compactification associated with the Eberlein algebra. It is called the Eberlein compactification and it can be constructed as the spectrum of the Eberlein algebra. The algebra of weakly almost periodic functions is one of the most important function spaces in the theory of topological semigroups. Both the weakly almost periodic functions and the associated weakly almost periodic compactification have been extensively studied since the 1930s. The Fourier-Stieltjes algebra, and hence its uniform closure, are subalgebras of the weakly almost periodic functions for any locally compact group. As a consequence, the Eberlein compactification is always a semitopological semigroup and a quotient of the weakly almost periodic compactification. We aim to study the structure and complexity of the Eberlein compactifications. In particular, we prove that for certain Abelian groups, weak^{*}-closed subsemigroups of L^{\infty}[0, 1] may be realized as quotients of their Eberlein compactifications, thus showing that both the Eberlein and weakly almost periodic compactifications are large and complicated in these situations. Moreover, we establish various extension results for the Eberlein algebra and Eberlein compactification and observe that levels of complexity of these structures mimic those of the weakly almost periodic ones. Finally, we investigate the structure of the Eberlein compactification for a certain class of non-Abelian, Heisenberg type locally compact groups and show that aspects of the structure of the Eberlein compactification can be relatively simple.