Algebraic Topology Seminar
Monday, September 18, 2023 at 4:30pm to 6:00pm
Building 2, 2-131
182 MEMORIAL DR, Cambridge, MA 02139
Title: Integral models for spaces
Abstract: Generalizing and building on the work of Kriz, Ekedahl, Goerss, Lurie, Mandell, Mathew, Mondal, Quillen, Sullivan, Toën and Yuan, I will describe an integral cochain model for nilpotent spacees of finite type. A binomial ring is a lambda-ring in which all Adams operations act as the identity. A derived binomial ring is a derived Λ-ring equipped with simultaneous trivializations of the commuting Adams operations. For example, if X is a space, then ZX, the integral cochains on X, is naturally a derived binomial ring. The induced contravariant functor from spaces to derived binomial rings is fully faithful when restricted to nilpotent spaces of finite type. This is related, closely, to recent work of Horel and of Kubrak—Shuklin—Zakharov.