Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 109-114).

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Dissertation (PhD)--University of Stellenbosch, 2007. / Bibliography. Also available via the Internet.

Made available in DSpace on 2014-06-11T19:27:09Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-11-10Bitstream added on 2014-06-13T18:30:56Z : No. of bitstreams: 1 dutra_acb_me_rcla.pdf: 707752 bytes, checksum: 003487414f094d392a97a22a4efb885b (MD5) / Neste trabalho tratamos do objeto matemático Grupo Topológico. Para este desenvolvimento, abordamos elementos básicos de Grupo e Espaço Topológico / In this work we consider the mathematical object Topological Group. For this development, we discuss the basic elements of the Group and Topological Space

Working at the prime p = 3, we construct a stably finite spectrum, Z, with a v_2^1 self map f. Further, both Ext_A(H*(Z),Z_3) and Ext_A(H*(Z),H*(Z)) have a vanishing line of slope 1/16 in (t-s,s) coordinates, and the map f is represented by an element a of Ext where multiplication by a is parallel to the vanishing line. To accomplish this construction, we prove a result about the connection between particular self maps of spectra and their effect on the Margolis homology of related modules over the Steenrod Algebra.

In his seminal work on modular curves and the Eisenstein ideal, Mazur studied the existence of congruences between certain Eisenstein series and newforms, proving that Eisenstein ideals associated to weight 2 cusp forms of prime level are locally principal. In this dissertation, we re-examine Eisenstein congruences, incorporating a notion of “depth of congruence,” in order to understand the local structure of Eisenstein ideals associated to weight 2 cusp forms of squarefree level N. Specifically, we use a commutative algebra result of Berger, Klosin, and Kramer to bound the depth of mod p Eisenstein congruences (from below) by the p-adic valuation of φ(N). We then show how this depth of congruence controls the local principality of the associated Eisenstein ideal.

We investigate quotient-fine nearness frames, showing that they are reflective in the category of strong nearness frames, and that, in those with spatial completion, any near subset is contained in a near grill. We construct two categories, each of which is shown to be equivalent to that of quotient-fine nearness frames. We also consider some subcategories of the category of nearness frames, which are co-hereditary and closed under coproducts. We give due attention to relations between these subcategories. We introduce totally strong nearness frames, whose category we show to be closed under completions. We investigate N-homomorphisms and remote points in the context of totally bounded uniform frames, showing the role played by these uniform N-homomorphisms in the transfer of remote points, and their relationship with C -quotient maps. A further study on grills enables us to establish, among other things, that grills are precisely unions of prime filters. We conclude the thesis by showing that the lattice of all nearnesses on a regular frame is a pseudo-frame, by which we mean a poset pretty much like a frame except for the possible absence of the bottom element. / Mathematical Sciences / Ph.D. (Mathematics)

Made available in DSpace on 2015-04-09T12:28:21Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-02-28Bitstream added on 2015-04-09T12:48:18Z : No. of bitstreams: 1 000810685.pdf: 423114 bytes, checksum: d115e8de0825c2a98f8531e8d0a39ce2 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / A fibração de Milnor aparece como a principal ferramenta no estudo local da topologia das singularidades analíticas reais e complexas. Neste trabalho estudaremos o Teorema de Fibração de Milnor e o surpreendente comportamento topológico das Fibras de Milnor. Para tais objetivos, usaremos algumas ferramentas da Geometria Algébrica, Análise Complexa em várias variáeis e um pouco da Teoria de Morse / The Milnor bration appears as the main tool in the topological local study of real and complex analytic singularities. In this work we study the famous Milnor Fibration Theorem, and the surprising topological behavior of the Milnor bres. To reach these objectives we use some tools of classical Algebraic Geometry, Complex Analysis of several variables and also some aspects of Morse Theory

Orientador: João Carlos Ferreira Costa / Banca: Ana Claudia Nabarro / Banca: Luciana de Fátima Martins / Resumo: A fibração de Milnor aparece como a principal ferramenta no estudo local da topologia das singularidades analíticas reais e complexas. Neste trabalho estudaremos o Teorema de "Fibração" de Milnor e o surpreendente comportamento topológico das Fibras de Milnor. Para tais objetivos, usaremos algumas ferramentas da Geometria Algébrica, Análise Complexa em várias variáeis e um pouco da Teoria de Morse / Abstract: The Milnor bration appears as the main tool in the topological local study of real and complex analytic singularities. In this work we study the famous Milnor Fibration Theorem, and the surprising topological behavior of the Milnor bres. To reach these objectives we use some tools of classical Algebraic Geometry, Complex Analysis of several variables and also some aspects of Morse Theory / Mestre

Orientador: Thiago de Melo / Banca: Alice Kimie Miwa Libardi / Banca: Oziride Manzoli Neto / Resumo: O objetivo deste trabalho é estudar grande parte do artigo [6], no qual Gottlieb define o subgrupo G(X, x0) de 'pi'1(X, x0) (em que X é um CW-complexo conexo por caminhos), posteriormente chamado de "grupo de Gottlieb"; o calculamos para diversos espaços, como as esferas, o toro, os espaços projetivos, a garrafa de Klein, etc; posteriormente, estudamos o artigo [22] de Varadarajan, que generalizou o grupo de Gottlieb para um subconjunto G(A, X) de [A, X]*. Por fim, calculamos G(S[n], S[n]) / Abstract: The goal of this work is to study partialy the article [6], in which Gottlieb has defined a subgroup G(X, x0) of 'pi'1(X, x0) (where X is a path-connected CW-complex based at x0), called "Gottlieb group" in the literature. This group is computed in this work for some spaces, namely the spheres, the torus, the projective spaces, and the Klein bottle. Further, a paper by Varadarajan[22] who has generalized Gottlieb group to a subset G(A, X)of [A, X]* is studied. Finally, the groups G(S[n], S[n]) is computed / Mestre