Naslov
Existence and uniqueness of group structures on covering spaces over groups

Autori
Eda, Katsuya ; Matijević, Vlasta

Izvornik
Fundamenta mathematicae (0016-2736) 238 (2017), 3; 241-267

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
topological group ; compact group ; locally compact group ; abelian group ; compactly connected space ; locally compactly connected space ; covering map ; overlay map ; covering homomorphism

Sažetak
Let f:X->Y be a covering map from a connected space X onto a topological group Y and let x_0 be a point of X such that f(x_0) is the identity of Y. We examine if there exists a group operation on X which makes X a topological group with the identity x_0 and f a homomorphism of groups. We prove that the answer is positive in two particular cases: if f is an overlay map over a locally compact group or if Y is locally compactly connected. In this way we generalize previously obtained results for overlay maps over compact groups and covering maps over locally path-connected groups. Furthermore, we prove that in both cases the group structure on X is unique.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA