Group structure in finite coverings of compact solenoidal groups. (English) Zbl 0968.22002

Grigorian, S. A.; Gumerov, R. N.; Kazantsev, A. V.

Lobachevskii J. Math. 6, 39-46 (2000).

It is shown that for any \(n\)-fold covering \(p:X\to G\) of a compact solenoidal group \(G\) by a connected topological space \(X\) the space \(X\) admits a compatible topological group structure turning \(p\) into a homomorphism between compact Abelian groups. A topological group \(G\) is solenoidal provided it admits a continuous group homomorphism \(h:\mathbb R\to G\) from the additive group of real numbers whose image \(h(\mathbb R)\) is dense in \(G\).

Reviewer: Taras Banakh (Lviv)

MSC:

22A05	Structure of general topological groups
57M10	Covering spaces and low-dimensional topology

Keywords:

solenoidal group; covering; topological group structure