The dissertation uses a number of mathematical formula including de Rham cohomology with complex coefficients to state and prove extension of Brieskorn's Lemma theorem.

In algebraic topology, we work to classify objects. My research aims to build a better understanding of one important notion of classification of differentiable manifolds called cobordism. Cobordism is an equivalence relation, and the equivalence classes in cobordism form a graded ring, with operations disjoint union and Cartesian product. My dissertation studies this graded ring in two ways: 1. by attempting to find preferred class representatives for each class in the ring. 2. by computing the image of the ring under an interesting ring homomorphism called the Witten Genus.

We build a model structure from the simple point of departure of a structured interval in a monoidal category — more generally, a structured cylinder and a structured co-cylinder in a category.

No description available.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: p. 135-138. / by James William Walker. / Ph.D.

The goal of this thesis is to give an introduction to the geometric picture of bivariant K-theory developed by Emerson and Meyer building on the ideas Connes and Skandalis, and then to apply this machinery to give a geometric proof of a result of Emerson. We begin by giving an overview of topological K-theory, necessary for developing bivariant K-theory. Then we discuss Kasparov's analytic bivariant K-theory, and from there develop topological bivariant K-theory. In the final chapter we state and prove the result of Emerson. / Graduate

Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-03-13Bitstream added on 2014-06-13T20:48:28Z : No. of bitstreams: 1 lima_af_me_sjrp.pdf: 566999 bytes, checksum: e8609221640cc685479db8cc71b941c4 (MD5) / Not available

Orientador: Ermínia de Lourdes Campello Fanti / Coorientador: Flávia Souza Machado da Silva / Banca: Pedro Luiz Queiroz Pergher / Banca: Maria Gorete Carreira Andrade / Resumo: O objetivo principal deste trabalho e estudar a relação entre cohomologia de grupos e o problema de classificar grupos wallpaper, que são grupos de simetrias de certas figuras do plano chamadas padrões wallpaper. Há, a menos de equivalência, exatamente 17 grupos wallpaper, que classificamos usando teoria dos grupos e algebra linear. Dado um grupo wallpaper G, temos associado inicialmente a G um subgrupo abeliano normal T (subgrupo das translações) chamado reticulado, um grupo G0 = G=T chamado grupo ponto, uma ação de G0 sobre T (de modo que T e um ZG0-m odulo) e uma extensão do grupo G0 por T , 0 ! T ! G ! G0 ! 0. Usando o fato de que existe uma correspondência biunívoca entre o segundo grupo de cohomologia, H2(G0; T ), e o conjunto das classes de equivalência de G0 por T que dão origem a ação induzida de G0 sobre T e computando H2(G0; T ), para as várias possibilidades para G0, apresentamos um limitante superior para o número de grupos wallpaper. Para o cálculo de H2(G0; T ), para certos grupos pontos G0, utiliza-se a sequência espectral cohomológica e a sequência exata de cinco termos / Abstract: The main goal of this work is to study the relation between the cohomology of groups and the problem of classifying wallpaper groups, which are symmetry groups of certain gures on the plane called wallpaper patterns. There are, up to isomorphism/equivalence, exactly 17 wallpaper groups, classi ed by using group theory and linear algebra. Given a wallpaper group G, we initially associate to G an abelian normal subgroup T (subgroup of the translations) called lattice, a group G0 = G T called point group, an action of G0 on T (in such a way that T is a ZG0-module) and an extension of the group G0 by T , 0 ����! T ����! G ����! G0 ����! 0. Using the fact that there is an one-to-one correspondence between the second cohomology of group, H2(G0; T ), and the set of equivalence classes of the extensions of G0 by T , that gives rise to the induced action of G0 on T , and computing H2(G0; T ), for the sereval possibilities for G0, we present an upper bound for the number of wallpaper groups. For the calculation of H2(G0; T ), of certain point groups G0, it is used the cohomological spectral sequence and the ve terms exact sequence / Mestre

Orientador: Elíris Cristina Rizziolli / Banca: Edivaldo Lopes da Silva / Banca: João Peres Vieira / Resumo: Neste trabalho tratamos do objeto matemático Grupo Topológico. Para este desenvolvimento, abordamos elementos básicos de Grupo e Espaço Topológico / Abstract: In this work we consider the mathematical object Topological Group. For this development, we discuss the basic elements of the Group and Topological Space / Mestre

Orientador: Maria Gorete Carreira Andrade / Banca: Ermínia Lourdes Campello Fanti / Banca: Ligia Laís Fêmina / Resumo: Não disponível / Abstract: Not available / Mestre