Naslov
On covering maps over the product of two solenoids

Autori
Matijević, Vlasta

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

Izvornik
4th Croatian Mathematical Congress CroMC2008 Abstracts / - Osijek, 2008, 42-42

Skup
4th Croatian Mathematical Congress CroMC2008

Mjesto i datum
Osijek, Hrvatska, 17.06.2008. - 20.06.2008

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
covering map; compact abelian group; solenoid; Klein bottle; weak solenoidal space

Sažetak
For a sequence p=(p_{;i};) of positive integers p_{;i};, let Σ (p) denote a solenoid obtained by the sequence p. We consider finite-sheeted covering maps over the product Σ (p)×Σ (r) of two solenoids and in some particular cases examine under which conditions total spaces are homeomorphic to the base space Σ (p)×Σ (r). We show that a compact connected 2-dimensional abelian group X covers a Klein bottle weak solenoidal space (i.e. the inverse limit of an inverse sequence, where each term is a Klein bottle K and each bonding map is a covering map over K) if and only if X covers the product Σ (p)×Σ (r) of two solenoids and at least one of the sequences p and r consists of odd integers. This enables us to answer the following question: Does every compact connected 2-dimensional abelian group X cover Klein bottle weak solenoidal spaces ? We answer the question in the negative. Moreover, we give an example of a group that covers groups with any finite number of sheets but does not cover any Klein bottle weak solenoidal space.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA