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Pregled bibliografske jedinice broj: 672057

Zbornik radova

Autori: Matijević, Vlasta
Naslov: Overlay structures and covering homomorphisms
Izvornik:
Skup: International Conference on the Topology and Geometry 2013 Joint with the Sixth Japan-Mexico Topology Symposium
Mjesto i datum: Matsue, Japan, 02-06. 09. 2013.
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).
Vrsta sudjelovanja: Pozvano
Vrsta prezentacije u zborniku: Sažetak
Vrsta recenzije: Međunarodna recenzija
Projekt / tema: 177-0372791-0886
Izvorni jezik: ENG
Kategorija: Znanstveni
Znanstvena područja:
Matematika
Upisao u CROSBI: Vlasta Matijević (vlasta@pmfst.hr), 3. Sij. 2014. u 18:56 sati



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