Topology Seminar: Motivic infinite loop spaces

Given a topological space X, May’s recognition principle says that a structure of infinite loop space on X is equivalent to a group-like $E_\infty$-monoid structure.  We will discuss an analogous result in motivic homotopy theory which says that a structure of infinite P^1-loop space on a motivic space X is equivalent to a homotopy coherent system of certain transfer maps.  This is based on an analogue of the Pontrjagin-Thom construction which identifies stable homotopy groups of spheres with groups of framed bordisms.  This is joint work with E. Elmanto, M. Hoyois, V. Sosnilo and M. Yakerson.