Naslov
On covering homomorphisms

Autori
Matijević, Vlasta

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, ostalo

Izvornik
24th Summer Conference on Topology and Its Applications, Book of abstracts / - Brno, 2009, 12-13

ISBN
978-80-904020-3-4

Skup
24th Summer Conference on Topology and Its Applications

Mjesto i datum
Brno, Češka Republika, 14.07.2009. - 17.07.2009

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Covering map; covering homomorphism; topological group; overlay map

Sažetak
Let Y be a connected group and let f:X→Y be a covering map from a connected space X. We say that f is a covering homomorphism if it is possible to define a multiplication ⋅ on X in such a way that X becomes a topological group and f becomes a homomorphism of topological groups. It is well-known that each covering map f:X→Y from a pathwise connected space X on a pathwise connected, locally pathwise connected group Y is a covering homomorphism. In 1972, R.H. Fox introduced a notion of on overlay map in order to extend the classical classification theorem for covering maps to arbitrary connected metric spaces. Using shape-theoretic techniques we show that a covering map f:X→Y on a compact connected group Y is a covering homomorphism if and only if f is an overlay map. In particular, each finite-sheeted covering map f:X→Y on a compact connected group Y is a covering homomorphism.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA