Nuclear and minimal atomic S-algebras

• Main Author: Gilmour, Helen S. E.
• Published: University of Glasgow 2006
• Subjects: 512; QA Mathematics
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.433267

We begin in Chapter 1 by considering the original framework in which most work in stable homotopy theory has taken place, namely the stable homotopy category. We introduce the idea of structured ring and module spectra with the definition of ring spectra and their modules. We then proceed by considering the category of S-modules MS constructed in [19]. The symmetric monoidal category structure of MS allows us to discuss the notions of S-algebras and their modules, leading to modules over an S-algebra R. In Section 2.5 we use results of Strickland [43] to prove a result relating to the products on ko/? as a ko-module. A survey of results on nuclear and minimal atomic complexes from [5] and [23] is given in the context of MS in Chapter 3. We give an account of basic results for topological André-Quillen homology (HAQ) of commutative S-algebras in Chapter 4. In Section 4.2 we are able to set up a framework on HAQ for cell commutative S-algebras which allows us to extend results reported in Chapter 3 to the case of commutative S-algebras in Chapter 5. In particular, we consider the notion of a core of commutative S-algebras. We give examples of non-cores of MU, MSU, MO and MSO in Chapter 6. We construct commutative MU-algebra MU//x2 in Chapter 7 and consider various calculations associated to this construction.