On Spaces of Coverings

Abstract: Consider a relation $R\subset X\times Y$ between two topological spaces. A finite collection $C=(x_1,\ldots,x_n)\in X^n$ is a covering if for any $y\in Y$, one has $(x_k,y)\in R$ for one of the points $x_k$ in $C$. (For example, if $X=Y$ is a metric space, and $R$ is the relation of being at the distance $<\epsilon$, then $C$ is a covering if the union of $\epsilon$-balls around $x_k$'s cover $Y$.) The topology of the space of coverings $C_R(n)$ is important, if unexplored, topic in several applied disciplines, from multi-agent systems to sociology. In this talk we discuss some examples where the homotopy type of these spaces can be explicitly computed.

geometric topology

Audience: researchers in the topic

( video )

GEOTOP-A seminar

Series comments: Web-seminar series on Applications of Geometry and Topology