Title: A multiplicative comparison of Segal and Waldhausen K-theory
Speaker: Anna Marie Bohmann
Speaker Info: Vanderbilt University
Brief Description:
Special Note:
Abstract:
In influential work of the 70s and 80s, Segal and Waldhausen each construct a version of K-theory that produces spectra from certain types of categories. These constructions agree, in the sense that appropriately equivalent categories yield weakly equivalent spectra. In the 2000s, work of Elmendorf--Mandell and Blumberg--Mandell produced more structured versions of Segal and Waldhausen K-theory, respectively. These versions are "multiplicative," in the sense that appropriate notions of pairings of categories yield multiplication-type structure on their resulting spectra. In this talk, I will discuss joint work with Osorno in which we show that these constructions agree as multiplicative versions of K-theory. Consequently, we get comparisons of rings spectra built from these two constructions. Furthermore, the same result also allows for comparisons of related constructions of spectrally-enriched categories.Date: Monday, June 03, 2019