The Oriented Freudenthal Suspension TheoremMPIM

by Thorger Geiß (Universität Münster)

Tuesday May 26, 2026, 11:00 AM → 12:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Seminar Room (Max Planck Institute for Mathematics)

Abstract Homotopy Theory Seminar

The classical Freudenthal Suspension Theorem is the statement that, given a space X, the connectivity of the unit map X -> ΩΣX of the loop-suspension adjunction is (roughly) twice the connectivity of X. In this talk, I will discuss the setting of oriented (or directed) homotopy theory, in which spaces are replaced by higher, i.e. (∞,ω)-, categories and the cartesian product by the Gray tensor product, and generalize the Freudenthal Suspension Theorem in this context. This gives, in particular, evidence for a yet-elusive "oriented topos theory".