Seminars: I. Baskov, Properties of the functor which changes the topological subgroup $\mathbb R^\delta$ to $\mathbb R$

SEMINARS


V. A. Rohlin St. Petersburg Topology Seminar March 4, 2019 17:15, St. Petersburg, POMI, room 311 (27 Fontanka)

Properties of the functor which changes the topological subgroup $\mathbb R^\delta$ to $\mathbb R$ I. Baskov St. Petersburg State University, Mathematics and Mechanics Faculty
Abstract: Consider the pushout functor $$ \mathbb R _{\mathbb R^\delta} {-} $$ from the under-category $\mathbb R^\delta$-TGrp of topological groups under $\mathbb R$ with discrete topology to the under-category $\mathbb R$-TGrp of topological groups under $\mathbb R$. We will investigate basic properties of this functor, such as homotopy properties and the presentation of $\mathbb R _{\mathbb R^\delta} X$ as the colimit of a sequence $F^1(X)\to F^2(X) \to \dots$. We also state the problem of the calculation of the cohomology groups $$ H^* (\mathbb R *_{\mathbb R^\delta} X;\mathbb{F} _p) $$ and provide this calculation for central and normal morphisms $\mathbb R^\delta\to X$.