Thesis (Ph. D.)--University of Oregon, 2001. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 98-99). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p3025008.

Thesis (doctoral)--Friedrichs-Universität Halle-Wittenberg, 1912. / Vita. Includes bibliographical references (p. [74]-86).

No description available.

This thesis consists of two parts, both being concerned with operads related to the ribbon braid groups. In the first part, we define a notion of semidirect product for operads and use it to study the framed $n$-discs operad (the semidirect product $f\mathcal{D}_n=\mathcal{D}_n\rtimes SO(n)$ of the little $n$-discs operad with the special orthogonal group). This enables us to deduce properties of $f\mathcal{D}_n$ from the corresponding properties for $\mathcal{D}_n$. We prove an equivariant recognition principle saying that algebras over the framed $n$-discs operad are $n$-fold loop spaces on $SO(n)$-spaces. We also study the operations induced on homology, showing that an $H(f\mathcal{D}_n)$-algebra is a higher dimensional Batalin-Vilkovisky algebra with some additional operators when $n$ is even. Contrastingly, for $n$ odd, we show that the Gerstenhaber structure coming from the little $n$-discs does not give rise to a Batalin-Vilkovisky structure. We give a general construction of operads from families of groups. We then show that the operad obtained from the ribbon braid groups is equivalent to the framed 2-discs operad. It follows that the classifying spaces of ribbon braided monoidal categories are double loop spaces on $S^1$-spaces. The second part of this thesis is concerned with infinite loop space structures on the stable mapping class group. Two such structures were discovered by Tillmann. We show that they are equivalent, constructing a map between the spectra of deloops. We first construct an `almost map', i.e a map between simplicial spaces for which one of the simplicial identities is satisfied only up to homotopy. We show that there are higher homotopies and deduce the existence of a rectification. We then show that the rectification gives an equivalence of spectra.

We prove two theorems concerning the action of the Steenrod algebra in cohomology and homology. (i) Let A denote a finitely generated graded F_p polynomial algebra over the Steenrod algebra whose generators have dimensions not divisible by p. The possible sets of dimensions of the generators for such A are known. It was conjectured that if we replaced the polynomial algebra A by a polynomial algebra truncated at some height greater than p over the Steenrod algebras, the sets of all possible dimensions would coincide with the former list. We show that the conjecture is false. For example F₁₁[x₆,x₁₀]¹² truncated at height 12 supports an action of the Steenrod algebra but F₁₁[x₆,x₁₀] does not. (ii) Let V be an elementary abelian 2-group of rank 3. The problem of determining a minimal set of generators for H*(BV,F₂) over the Steenrod algebra was an unresolved problem for many years. (A solution was announced by Kameko in June 1990, but is not yet published.) A dual problem is to determine the subring M of the Pontrjagin ring H*(BV,F₂). We determine this ring completely and in particular give a verification that the minimum number of generators needed in each dimension in cohomology is as announced by Kameko, but by using completely different techniques. Let v ε V - (0) and denote by a_5(v) ε H*(BV,F₂) the image of the non-zero class in H_2s-1(RP^∞,F₂) imeq F₂ under the homomorphism induced by the inclusion of F_{2 → V onto (0,v). We show that M is isomorphic to the ring generated by (a}_s(v),s ≥ 1, v ε V - (0)) except in dimensions of the form 2^r+3 + 2^r+1 + 2^r - 3, r ≥ 0, where we need to adjoin our additional generator.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Typescript. Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2003. / Includes bibliographical references. Also available on the Internet.

Thesis (doctoral)--Université des sciences et techniques de Lille I. / "No. d'ordre : 535." Includes bibliographical references.