Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Let K(,*)(A; /L('n)) denote the mod-L('n) algebraic K-theory of a 1/L -algebra A. V. Snaith has studied Bott-periodic algebraic K-theory K(,i)(A; /L('n)) 1/(beta)(,n) , the direct limit of iterated multiplications by (beta)(,n), the 'Bott element', using the K-theory product. For L an odd prime, Snaith has given a description of K(,*)(A; /L('n))(1/(beta)(,n)) using Adams maps between Moore spectra. These constructions are interesting, in particular, for their connections with the Lichtenbaum-Quillen conjecture.;In this thesis we obtain an analogous description of K(,*)(A; /2('n)) 1/(beta)(,n) , n (GREATERTHEQ) 2, for an algebra A with 1/2 (ELEM) A and such that A contains a fourth root of unity. We approach this problem using low dimen- sional computations of the stable homotopy groups of B /4, and transfer arguments to show that a power of the mod-4 'Bott element' is induced by an Adams map.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.