Naslov
Overlay structures and covering homomorphisms

Autori
Matijević, Vlasta

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

Skup
International Conference on the Topology and Geometry 2013 Joint with the Sixth Japan-Mexico Topology Symposium

Mjesto i datum
Matsue, Japan, 02.09.2013. - 06.09.2013

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Overlay map; covering map; overlay structure; covering homomorphism; compact group.

Sažetak
In 1972 R. H. Fox extended the classical classification theorem for covering maps to arbitrary connected metric spaces. However, he had to restrict covering maps to a narrower class, called overlay maps. In 1978 T. T. Moore introduced the notion of an overlay structure and exhibited examples of overlay maps over metric continua which admit different overlay structures. Using the shape-theoretic technique of ANR-resolutions we give a classification theorem for overlay structures by proving that there is a bijection between the set of all pointed equivalence classes of s-sheeted indecomposable overlay structures over a connected space Y and the set of all subprogroups of index s of the fundamental progroup of Y (S. Mardešić and V. Matijević). An application of this theorem shows that, for a connected overlay map f:X→Y over a compact connected group Y, every overlay structure admits a unique multiplication on X which makes X a topological group and makes f a covering homomorphism. In particular, we study covering maps over 1-dimensional and 2-dimensional compact connected abelian groups and exhibit examples which show that compact connected groups are not self-covering spaces and a covering map need not be a covering homomorphism (K. Eda and V. Matijević).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA