Семинары: Г. С. Макеев, On Kasparov-type homotopy functors for $C^\ast$-algebras (PhD dissertation discussion)

СЕМИНАРЫ


Функциональный анализ и его приложения 14 сентября 2023 г. 08:30, г. Ташкент, Онлайн на платформе Zoom (ID: 3078301000, Password: 1)

On Kasparov-type homotopy functors for $C^\ast$-algebras (PhD dissertation discussion) G. S. Makeev^ab ^a Lomonosov Moscow State University ^b V. I. Romanovskiy Institute of Mathematcs of the Academy of Sciences of Uzbekistan, Tashkent
Аннотация: Many constructions involving asymptotic homomorphisms in Connes-Higson $E$-theory can be lifted at the level of natural transformations between endofunctors of $C^\ast$-algebras. For such natural transformations we introduce the notion of homotopy and define a category with objects good enough endofunctors and morphisms homotopy classes of natural transformations. Objects of this category induce generalized homotopies of $\ast$-homomorphisms, which can be used to obtain an unsuspended description of $E$-theory and $E$-theoretical analog of $C^\ast$-algebra extension groups. The machinery can also be applied for computing $K$-homology. Website: https://us02web.zoom.us/j/3078301000