by Leung Chi Wai. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaf [51]

Orientador: João Carlos Ferreira Costa / Banca: Aldício Jos e Miranda / Banca: Luciana de Fátima Martins / Resumo: O objetivo da dissertação e estudar a equivalência de contato, ou K-equivalência, introduzida por John Mather como ferramenta da teoria de Singularidades para classificar seus objetos. Mostraremos como a equivalência de contato esta relacionada com a Geometria e a Topologia. Com a Geometria, através do estudo do contato entre pares de certas subvariedades em Rn. Com a Topologia, através da versão topológica da K-equivalência, a chamada C0-K-equivalência, observando que o grau e um invariante completo no caso de germes de aplicações f : (Rn;0) - (Rn;0) / Abstract: The goal of this work is to study the notion of contact equivalence, or K-equivalence, introduced by John Mather in the Singularity theory. We will show how the contact equivalence is related to Geometry and Topology. With the Geometry through the study of the contact between pairs of certain submanifolds in Rn. With the Topology through the topological version of K-equivalence, the called C0-K-equivalence, observing that the degree is a complete invariant in the case of map germs f : (Rn;0) - (Rn;0) / Mestre

We define an extension of the nth homotopy group which can distinguish a larger class of spaces. (E.g., a converging sequence of disjoint circles and the disjoint union of countably many circles, which have isomorphic fundamental groups, regardless of choice of basepoint.) We do this by introducing a generalization of homotopies, called component-homotopies, and defining the nth extended homotopy group to be the set of component-homotopy classes of maps from compact subsets of (0,1)n into a space, with a concatenation operation. We also introduce a method of tree-adjoinment for "connecting" disconnected metric spaces and show how this method can be used to calculate the extended homotopy groups of an arbitrary metric space.

Mémoire rédigé en vue de l'obtention de l'habilitation à diriger les recherches. Il donne un résumé de mon activité de recherche (anneaux de Chow, classes de Stiefel-Whitney, algèbres de Hopf, entrelacs, K-théorie de Milnor).

Let R be a connective ring spectrum and let M be an R-bimodule. In this paper we prove several results that relate the K-theory of R⋉M and T[superscript M, subscript R] to a “topological Witt vectors” construction W(R; M), where R ⋉ M is the square-zero extension of R by M and T [superscript M, subscript R] is the tensor algebra on M. Our main results include a desciption of the Taylor tower of K(R ⋉ (−)) and the derived functor of K̃(TR(−)) on the category of R-bimodules in terms of the Taylor tower of W(R;−). W(R;−) has an easily described Taylor tower, given explicitly by Lindenstrauss and McCarthy in [17]. Our main results serve as generalizations of the results for discrete rings in [17, 18] and also extend the computations by Hesselholt and Madsen [15] showing that π₀(TR(R; p)) is isomorphic to the p-typical Witt vectors over R when R a commutative ring. / text

In this thesis, we establish a pair of systems of higher order cohomology operations that act on the Ζ_p-ordinary cohomology of spaces that are free of p-torsion. These "pyramids" of operations are generated by the p-divisibility of certain sums of "pseudo" primary cohomology operations that operate on the p-local cohomology of p-torsion-free spaces. The properties of these higher order operations allow us to prove theorems that either generalise or improve (in the sense of decreasing indeterminacy) several results in the literature.

Typescript. / Thesis (Ph. D.)--University of Hawaii, 1971. / Bibliography: leaves 73-74. / vi, 74 l

Thesis (Ph. D.)--University of Oregon, 2007. / Typescript. Includes vita and abstract. Includes bibliographical references (leaf 76). Also available for download via the World Wide Web; free to University of Oregon users.

Dissertation (Ph.D.)--Auburn University, / Abstract. Vita. Includes bibliographic references (p.88).

Thesis (M.S.)--University of Nevada, Reno, 2008. / "May, 2008." Includes bibliographical references (leaf 58). Online version available on the World Wide Web.