Thesis Defense
Tasos Moulinos
UIC
Topological $K$-theory and invertibility
Abstract: Topological K-theory of dg-categories is an invariant of $\mathbb{C}$-linear dg-categories
taking values in the $\infty$-category of $KU$-modules. I will describe a relative version
of this construction. Using this, I give a characterization, in terms of twisted $K$-theory, of the topological $K$-theory of the dg-category $Perf(X, A)$ of modules over an Azumaya algebra $A$ over $X$.
I then deduce a certain decomposition, for $X$ a finite CW-complex equipped with a bundle of projective
spaces $π : P → X$, of $KU(P)$ in terms of the twisted topological K-theory of $X$ ; this is
a topological analogue of a result of Quillen’s on the algebraic K-theory of Severi-Brauer
schemes.
Thursday April 19, 2018 at 4:30 PM in SEO 712