2020/03/26 by Andrew Baker, Baker, Andrew
Mathematics · Medicine · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Ophthalmology and Eye Disorders
paper · pdf · doi:10.48550/arxiv.2003.12003
Modern categories of spectra such as that of Elmendorf et al equipped with\nstrictly symmetric monoidal smash products allows the introduction of symmetric\nmonoids providing a new way to study highly coherent commutative ring spectra.\nThese have categories of modules which are generalisations of the classical\ncategories of spectra that correspond to modules over the sphere spectrum;\npassing to their derived or homotopy categories leads to new contexts in which\nhomotopy theory can be explored. In this paper we describe some of the tools\navailable for studying these `brave new homotopy theories' and demonstrate them\nby considering modules over the K-theory spectrum, closely related to\nMahowald's theory of bo-resolutions. In a planned sequel we will apply these\ntechniques to the much less familiar context of modules over the 2-local\nconnective spectrum of topological modular forms.\n