Online seminar, U. Haifa Topology & Geometry seminar on April 4, 2021
A recording of the talk is available here.
Topology & Geometry Seminar
Speaker: Shachar Carmeli, Weizmann Institute of Science
Topic: Higher semiadditivity and the K(1)-local sphere
Place: This is an online seminar. Please email David Blanc “blanc at math dot haifa dot ac dot il” for the Zoom ID and password.
Date: Sunday, April 4, 2021
Higher semiadditivity is a property of an infinity-category that allows, in particular, for the summation of families of morphisms between objects parametrized by pi-finite spaces.
Hopkins and Lurie showed that the K(n)-localizations of the infinity category of spectra are higher semiadditive. Consequently, by a work of Harpaz, the mapping objects in these infinity-categories admit the rich structure of higher commutative monoids.
While many abstract properties of these higher commutative monoids are known, explicit computations in them have not been carried out so far.
In my talk, I will present a work in progress, joint with Allen Yuan, which gives such a computation in the K(1)-local category. Specifically, I will show how to use higher semiadditive versions of algebraic K-theory and Grothendieck-Witt theory to compute these integration maps for the K(1)-local sphere.