Following Hopkins and Singer, we give a definition for the differential equivariant K-theory of a smooth manifold acted upon by a finite group. The ring structure for differential equivariant K-theory is developed explicitly. We also construct a pushforward map which parallels the topological pushforward in equivariant K-theory. An analytic formula for the pushforward to the differential equivariant K-theory of a point is conjectured, and proved in the boundary case and for ordinary differential K-theory in general. The latter proof is due to K. Klonoff. / text

Thesis (Ph. D.)--University of Texas at Austin, 2009. / Title from PDF title page (University of Texas Digital Repository, viewed on Sept. 17, 2009). Vita. Includes bibliographical references.

Thesis (Ph. D.)--State University of New York at Binghamton, Department of Mathematical Sciences, 2004. / Includes bibliographical references.

Let KO(X) be the real and KSP(X) be the quaternionic K-theory of a finite CW-complex X . The tensor product and the exterior powers of vector bundles induce on L(X) = KO(X) ⊕ KSP(X) the structure of Z₂ -graded λ-ring. In this thesis it is shown, that the Adams operations Ѱk : L(X) → L(X) , k = l, 2, 3,..., which are associated to this λ-ring, are ring homomorphisms and satisfy the composition law Ѱk ₀ Ѱℓ = Ѱℓk = Ѱℓ ₀ Ѱk , k, ℓ = 1, 2, 3,... Finally, the ring L(X) together with its Ѱ-operations is explicitely determined for the quaternionic and complex projective spaces. / Science, Faculty of / Mathematics, Department of / Graduate

For T the circle group, we construct a differential refinement of T-equivariant K-theory. We first construct a de Rham model for delocalized equivariant cohomology and a delocalized equivariant Chern character based on [19] and [14]. We show that the delocalized equivariant Chern character induces a complex isomorphism. We then construct a geometric model for differential T-equivariant K-theory analogous to the model of differential K-theory in [27] and deduce its basic properties. / text

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

by Wong Wah Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 53-54). / Introduction --- p.2 / Chapter 1 --- Preliminaries --- p.3 / Chapter 1.1 --- A Summary on C*-algebras --- p.3 / Chapter 1.2 --- Hereditary C*-subalgebras --- p.5 / Chapter 1.3 --- C*-Inductive Limit --- p.7 / Chapter 1.4 --- Basic K-Theory of C*-algebras --- p.9 / Chapter 2 --- C*-algebras of Real Rank Zero --- p.14 / Chapter 2.1 --- Basic Properties of C*-algebras with Real Rank Zero --- p.14 / Chapter 2.2 --- Strongly Morita Equivalence and Extensions --- p.30 / Chapter 3 --- Simple C*-algebras --- p.42 / Chapter 3.1 --- Basic Properties --- p.42 / Chapter 3.2 --- Cuntz Algebras --- p.51 / Bibliography --- p.53

Thesis (Ph. D.)--University of Oregon, 2001. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 62-63). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2009. / Title from title screen (site viewed January 5, 2010). PDF text: vi, 65 p. : ill. ; 645 K. UMI publication number: AAT 3359857. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2009. / Title from title screen (site viewed January 5, 2010). PDF text: v, 69 p. ; 721 K. UMI publication number: AAT 3360497. Includes bibliographical references. Also available in microfilm and microfiche formats.