On K(1)-local SU-bordism [Elektronische Ressource] / vorgelegt von Holger Reeker

On K(1)-local SU-bordismDissertationzur Erlangung des Doktorgrades (Dr. rer. nat.)der Fakult¨at fur¨ Mathematikder Ruhr-Universit¨at Bochumvorgelegt vonDipl.-Math. Holger ReekerMai 2009ContentsChapter 1. Introduction and statement of results 5Chapter 2. Some homotopical algebra 91. Generalized cohomology theories and spectra 92. Symmetric spectra over topological spaces 113. Complex oriented theories and computational methods 144. Bousfield localization of spectra 155. Algebraic manipulations of spectra 186. A resolution of the K(1)-local sphere 207. Thom isomorphism 21Chapter 3. The algebraic structure of K(1)-local E ring spectra 23∞1. Operads 232. Dyer-Lashof operations for K(1)-local E spectra 25∞3. The θ-algebra structure of π K∧MU 2604. The θ str of π K∧MSU 290Chapter 4. Splitting off an E summand T 31∞ ζ1. The image of MSU →MU 32∗ ∗2. Formal group laws and Miscenkos formula 34ˆ3. Construction of an SU-manifold with A = 1 384. Constr of an Artin-Schreier class 415. Construction of an E map T →MSU 41∞ ζ6. Split map - direct summand argument 420Chapter 5. Detecting free E summands TS 45∞1. Introduction to Adams operations in K-theory 45∞2. Calculating operations on K CP 47∗3. Bott’s formula and cannibalistic classes 524. Spherical classes in K MSU 55∗5. Umbral calculus 57Chapter 6.